{"id":177544,"date":"2022-06-02T15:15:00","date_gmt":"2022-06-02T09:45:00","guid":{"rendered":"https:\/\/www.aakash.ac.in\/blog\/?post_type=web-story&#038;p=177544"},"modified":"2022-09-03T11:10:19","modified_gmt":"2022-09-03T05:40:19","slug":"maths-symmetric-matrix-definition-with-examples-ncert-concept","status":"publish","type":"web-story","link":"https:\/\/www.aakash.ac.in\/blog\/web-stories\/maths-symmetric-matrix-definition-with-examples-ncert-concept\/","title":{"rendered":"Symmetric Matrix Definition With Examples | NCERT Maths Concept"},"content":{"rendered":"<p><html amp=\"\" lang=\"en\"><head><meta charSet=\"utf-8\"\/><meta name=\"viewport\" content=\"width=device-width,minimum-scale=1,initial-scale=1\"\/><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0.js\"><\/script><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0\/amp-story-1.0.js\" custom-element=\"amp-story\"><\/script><link 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vertical-align: middle;\n                border-radius: 15px;\n                background: rgba(11, 11, 11, 0.6);\n                color: rgba(255, 255, 255, 1);\n                font-family: -apple-system, BlinkMacSystemFont, \"Segoe UI\", Roboto, Oxygen-Sans, Ubuntu, Cantarell, \"Helvetica Neue\", sans-serif;;\n                font-size: calc(4 * var(--story-page-vw));\n                line-height: 1.4;\n                word-break: break-word;\n                word-wrap: break-word;\n                overflow-wrap: break-word;\n              }\n              <\/style>\n<p><meta name=\"web-stories-replace-head-start\"\/><title>Symmetric Matrix Definition With Examples | NCERT Maths Concept<\/title><link rel=\"canonical\" href=\"https:\/\/www.aakash.ac.in\/blog\/web-stories\/maths-symmetric-matrix-definition-with-examples-ncert-concept\/\"\/><meta name=\"web-stories-replace-head-end\"\/><\/head><body><amp-story standalone=\"\" publisher=\"Aakash BYJU&amp;#039;S Blog\" publisher-logo-src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/blue.png\" title=\"Symmetric Matrix Definition With Examples | NCERT Maths Concept\" poster-portrait-src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/cropped-Symmetric-matrix-1.jpg\"><amp-story-page id=\"568b5f37-c29f-440f-8679-4637776b9f67\" auto-advance-after=\"9s\"><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#253c44\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-6d922d4b-4914-4369-a76f-d25e7a8fa2cd\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img 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style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:1.1627906976744187% 1.1627906976744187% 1.1627906976744187% 1.1627906976744187% \/ 8% 8% 8% 8%;background-clip:content-box;background-color:rgba(0,0,0,0.7)\" id=\"el-aa311f0e-8b37-4a10-a844-9b5bf1850fd1\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.12263808139534883% 0;font-family:&quot;Roboto&quot;,&quot;Helvetica Neue&quot;,&quot;Helvetica&quot;,sans-serif;font-size:0.242718em;line-height:1.2;text-align:initial;padding:2.3255813953488373% 4.651162790697675%;color:#000000\"><span><span style=\"color: #fff\">BY Team Aakash Byju&#8217;s<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:12.13592%;top:74.11003%;width:76.45631%;height:14.88673%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6349206349206349% 0.6349206349206349% 0.6349206349206349% 0.6349206349206349% \/ 2.1739130434782608% 2.1739130434782608% 2.1739130434782608% 2.1739130434782608%\" id=\"el-8d19cf2a-e493-45fb-9f83-a4b9f1bef8dd\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.22619047619047575% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.404531em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #edf6f6\">Symmetric Matrix Definition With Examples<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:12.13592%;top:93.04207%;width:76.45631%;height:4.04531%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6349206349206349% 0.6349206349206349% 0.6349206349206349% 0.6349206349206349% \/ 8% 8% 8% 8%\" id=\"el-fe22062a-9a81-46c7-87b7-03942a3e03e4\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.18095238095238048% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.323625em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #edf6f6\">&nbsp;NCERT Maths Concept<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:10.92233%;top:72.3301%;width:76.69903%;height:1.13269%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-8a4007b8-de83-4611-af8e-86e250f5f078\">\n<div class=\"fill\" style=\"background-color:#c4c4c4;will-change:transform\"><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:98.86731%;width:76.69903%;height:1.13269%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-d7c93611-2195-4d8e-a991-f4b4e256e0ba\">\n<div class=\"fill\" style=\"background-color:#c4c4c4;will-change:transform\"><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:10.92233%;top:90.12945%;width:76.69903%;height:0.80906%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-d7382849-dddb-4071-8e22-17373eef568a\">\n<div class=\"fill\" style=\"background-color:#c4c4c4;will-change:transform\"><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:10.92233%;top:16.01942%;width:80.09709%;height:53.72168%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-3bdcfdfa-e2e2-4001-b554-32a9a3e9e677\">\n<div style=\"position:absolute;width:100%;height:176.70684%;left:0%;top:-38.35342%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/symmetric-matrix.png\" alt=\"symmetric matrix\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/symmetric-matrix.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/symmetric-matrix-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/symmetric-matrix-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/symmetric-matrix-150x267.png 150w\" sizes=\"(min-width: 1024px) 36vh, 80vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:0;width:14.07767%;height:9.38511%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-9c17788e-dbdd-4d3f-8722-efa3d7186f39\">\n<div style=\"position:absolute;width:100%;height:100.00004%;left:0%;top:-0.00002%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG.png\" alt=\"Aakash Icon Blue PNG\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG.png 96w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG-75x75.png 75w\" sizes=\"(min-width: 1024px) 6vh, 14vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"ba32cf7f-c1a0-4cfc-8809-86014de66f4d\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-5e2aed03-a364-4af6-942d-13a435136b6c\",\"keyframes\":{\"transform\":[\"translate3d(-114.92064%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-a911604b-cd36-4276-81a3-19df0bc30036\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" 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src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44.jpg\" alt=\"44\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:0;width:76.45631%;height:25.72816%;opacity:1\">\n<div id=\"anim-5e2aed03-a364-4af6-942d-13a435136b6c\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-114.92064%, 0px, 0)\">\n<div id=\"anim-a911604b-cd36-4276-81a3-19df0bc30036\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-9224d977-6230-4d08-bd12-a7b072393c33\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6349206349206349% 0.6349206349206349% 0.6349206349206349% 0.6349206349206349% \/ 1.257861635220126% 1.257861635220126% 1.257861635220126% 1.257861635220126%\" id=\"el-f132b5e0-e9cf-46e5-8ecb-4865c4fb24d1\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.1990476190476187% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">First let&#8217;s start with the definition of \u2018symmetric matrix\u2019 and then we will learn how to check whether a given matrix is symmetric or not.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:7.52427%;top:25.56634%;width:80.09709%;height:69.25566%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-9d1e2009-7eac-42b5-977d-83c945705db9\">\n<div style=\"position:absolute;width:100%;height:137.07166%;left:0%;top:-18.53583%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" 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type=\"application\/json\">[{\"selector\":\"#anim-b0447b0f-dad9-444f-a3ff-a3ac11d97c90\",\"keyframes\":{\"transform\":[\"translate3d(-115.55555%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-88850602-824e-427a-b4e7-4be02e652269\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-40bff03c-8d64-477a-852f-e324858ddd19\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#f9fbfb\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-8f156420-a609-4423-95d6-bdd9a68490bb\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/58.jpg\" alt=\"58\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/58.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/58-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/58-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/58-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:11.48867%;width:76.45631%;height:17.31392%;opacity:1\">\n<div id=\"anim-b0447b0f-dad9-444f-a3ff-a3ac11d97c90\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-115.55555%, 0px, 0)\">\n<div id=\"anim-88850602-824e-427a-b4e7-4be02e652269\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-40bff03c-8d64-477a-852f-e324858ddd19\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6349206349206349% 0.6349206349206349% 0.6349206349206349% 0.6349206349206349% \/ 1.8691588785046727% 1.8691588785046727% 1.8691588785046727% 1.8691588785046727%\" id=\"el-444eed05-ec34-4d0a-95db-c0405443acb3\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.1990476190476187% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">To understand the concept of \u2018symmetric matrix\u2019 one must know the definition of &nbsp;transpose of a matrix.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:0;top:25.24272%;width:100%;height:69.57929%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-4119d4ee-ae68-462a-a3a1-f2b5b7e87e8d\">\n<div style=\"position:absolute;width:100%;height:170.33591%;left:0%;top:-35.16796%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-2-1.png\" alt=\"Symmetric matrix-2-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-2-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-2-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-2-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-2-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"378d2256-799e-4f37-b73f-2fcefdb243ef\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-dbbc935f-8ddf-4c4c-ab59-0b43365dc033\",\"keyframes\":[{\"offset\":0,\"transform\":\"translate3d(0, -707.778%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.29,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.45,\"transform\":\"translate3d(0, -199.0271736%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.61,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.71,\"transform\":\"translate3d(0, -67.6635768%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.8,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.85,\"transform\":\"translate3d(0, -25.409230200000003%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.92,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.96,\"transform\":\"translate3d(0, -11.0413368%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":1,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"}],\"delay\":0,\"duration\":1300,\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#284893\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-89535fd7-9663-45aa-83d8-039228cdf286\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Classroom-Artboard-4.jpg\" alt=\"Classroom-Artboard 4\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Classroom-Artboard-4.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Classroom-Artboard-4-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Classroom-Artboard-4-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Classroom-Artboard-4-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:69.41748%;width:76.94175%;height:12.94498%;opacity:1\">\n<div id=\"anim-dbbc935f-8ddf-4c4c-ab59-0b43365dc033\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(0, -707.778%, 0)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6309148264984227% 0.6309148264984227% 0.6309148264984227% 0.6309148264984227% \/ 2.5% 2.5% 2.5% 2.5%;background-clip:content-box;background-color:rgba(0,0,0,0.7)\" id=\"el-c0991e28-d38f-497a-af5a-20fa0af0fa84\"><a href=\"https:\/\/byjus.com\/aakash-byjus-free-trial-class\/?utm_source=seobanner&amp;utm_medium=4th-webstory&amp;utm_campaign=freeliveclasses\" data-tooltip-icon=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG-1.png\" data-tooltip-text=\"Register Now For Aakash BYJU&#x27;S Free Live Classes\" target=\"_blank\" rel=\"noreferrer noopener\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0\"><\/p>\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.13308359621451105% 0;font-family:&quot;Roboto&quot;,&quot;Helvetica Neue&quot;,&quot;Helvetica&quot;,sans-serif;font-size:0.485437em;line-height:1.2;text-align:center;padding:1.2618296529968454% 2.5236593059936907%;color:#000000\"><span><span style=\"font-weight: 700; color: #fff\">Click Here To Attend Free Trail Class<\/span><\/span><\/p>\n<p><\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-page-outlink layout=\"nodisplay\" cta-image=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG.png\"><a href=\"https:\/\/byjus-aakash.onelink.me\/GieR\/aakashwebstories\" rel=\"\">Download Aakash App<\/a><\/amp-story-page-outlink><\/amp-story-page><amp-story-page id=\"cf8413e8-8638-4f52-ab50-24cfd17449fa\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-61c8b3a4-26a2-4a71-8b51-3234e0f12f85\",\"keyframes\":{\"transform\":[\"translate3d(-115.55555%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-1fca6414-ca74-4a12-a099-eda1a6c6d418\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-9c5d2415-81f1-44ff-8da5-cec3f72e6982\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#0c0819\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-663cf56d-9c12-4c80-b88b-4c78d9dd70c8\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/38.jpg\" alt=\"38\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/38.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/38-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/38-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/38-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:3.72168%;width:76.45631%;height:25.88997%;opacity:1\">\n<div id=\"anim-61c8b3a4-26a2-4a71-8b51-3234e0f12f85\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-115.55555%, 0px, 0)\">\n<div id=\"anim-1fca6414-ca74-4a12-a099-eda1a6c6d418\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-9c5d2415-81f1-44ff-8da5-cec3f72e6982\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6349206349206349% 0.6349206349206349% 0.6349206349206349% 0.6349206349206349% \/ 1.25% 1.25% 1.25% 1.25%\" id=\"el-fca7fa23-9bd7-42ac-a7f5-7a5a8a198e26\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.1990476190476187% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">The transpose of a matrix is an operator that flips over its diagonal. i.e, rows and columns of a matrix are interchanged to get a transpose of the matrix.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:31.5534%;width:80.09709%;height:64.07767%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-ea2648fc-f17a-4e1c-9e0e-7826d4a19e65\">\n<div style=\"position:absolute;width:100%;height:148.14815%;left:0%;top:-24.07408%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-5-1-1.png\" alt=\"Symmetric matrix-5-1 (1)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-5-1-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-5-1-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-5-1-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-5-1-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 36vh, 80vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"43946efa-4942-4387-b717-5a141e0a7118\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-e3e989e2-fc8d-4af5-8965-34819563af32\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-af3f4632-7a34-479a-bcd3-5c180ad4ba0f\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-80ece824-b081-47a1-a926-b70d8f0ca17f\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-fe2e2bad-4978-4e12-a54d-c14a3335c690\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#42052c\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-71a09fe4-ee30-4e95-87be-1bee44c28adf\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/34.jpg\" alt=\"34\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/34.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/34-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/34-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/34-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:1.2945%;width:76.69903%;height:10.67961%;opacity:1\">\n<div id=\"anim-e3e989e2-fc8d-4af5-8965-34819563af32\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-af3f4632-7a34-479a-bcd3-5c180ad4ba0f\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 3.0303030303030303% 3.0303030303030303% 3.0303030303030303% 3.0303030303030303%\" id=\"el-e8af8083-4328-4f4f-93c7-55e6a5a6ec3a\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.5656645569620258% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.404531em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">Now consider the example given below:<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:80.42071%;width:76.69903%;height:19.41748%;opacity:1\">\n<div id=\"anim-80ece824-b081-47a1-a926-b70d8f0ca17f\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-fe2e2bad-4978-4e12-a54d-c14a3335c690\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.6666666666666667% 1.6666666666666667% 1.6666666666666667% 1.6666666666666667%\" id=\"el-ac3d2033-e30c-4985-a14f-73d9cb09da37\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.4977848101265824% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">Did you notice how the matrix looks after changing the rows into columns or the columns into rows?<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:9.70874%;top:21.52104%;width:80.09709%;height:47.08738%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-007df4a6-f24d-4e2d-a689-061c41c51414\">\n<div style=\"position:absolute;width:100%;height:201.60367%;left:0%;top:-19.33944%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Symmetric-matrix-10-1-1.png\" alt=\"Symmetric matrix-10-1 (1)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Symmetric-matrix-10-1-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Symmetric-matrix-10-1-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Symmetric-matrix-10-1-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Symmetric-matrix-10-1-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 36vh, 80vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"b23efef2-26d6-41b1-9148-63ed8991b99e\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-e5157588-94dd-4aba-a5cc-f1bd0a4261ae\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-f222f3d5-0793-4cd3-a864-f53340f48910\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-23ecac8f-c27f-42a1-a0c2-9ee29b07eba7\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-c247fa8b-dd27-4d15-953f-6d386b006837\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#2f2d2a\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-f0510cfc-4ab1-4737-9565-956f469b0459\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/42.jpg\" alt=\"42\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/42.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/42-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/42-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/42-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:11.97411%;width:76.69903%;height:19.41748%;opacity:1\">\n<div id=\"anim-e5157588-94dd-4aba-a5cc-f1bd0a4261ae\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-f222f3d5-0793-4cd3-a864-f53340f48910\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.6666666666666667% 1.6666666666666667% 1.6666666666666667% 1.6666666666666667%\" id=\"el-1da4d649-875a-44a4-9e58-4d76dd15e723\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.4977848101265824% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">Yes, it looks the same as the input matrix. This type of matrix is called a symmetric matrix.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:36.40777%;width:76.21359%;height:63.59223%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-9b04e088-5b35-401e-9ac0-91f4634e5856\">\n<div style=\"position:absolute;width:100%;height:142.04128%;left:0%;top:-5.6556%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-6-1.png\" alt=\"Symmetric matrix-6-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-6-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-6-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-6-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-6-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 34vh, 76vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:26.69903%;top:70.55016%;width:77.18447%;height:4.36893%;opacity:1\">\n<div id=\"anim-23ecac8f-c27f-42a1-a0c2-9ee29b07eba7\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-c247fa8b-dd27-4d15-953f-6d386b006837\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.628930817610063% 0.628930817610063% 0.628930817610063% 0.628930817610063% \/ 7.4074074074074066% 7.4074074074074066% 7.4074074074074066% 7.4074074074074066%\" id=\"el-5e89df3d-43d3-4e16-98dc-a1915e00825b\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.47216981132075475% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.339806em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"bfeba4cf-8e0d-47bb-97e6-671bcfe35fd2\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-ad68be48-9d95-49d1-8af1-2c6bd2bf2544\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-a70c2833-8b8f-4aa7-9803-8e05de8dc9a8\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-1374be52-def8-4fbe-9204-9ff5447c1ced\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-443a0ee5-8f03-496b-93bc-009e986f4e52\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-87a086ca-9157-4e59-8afd-2a5f383bf51d\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-040e6782-0a7f-40c0-b034-85522c55a30f\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#545454\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-44f13477-6693-4a28-8d35-a0e5aae8cf6b\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/55.jpg\" alt=\"55\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/55.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/55-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/55-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/55-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:3.39806%;width:76.94175%;height:9.38511%;opacity:1\">\n<div id=\"anim-ad68be48-9d95-49d1-8af1-2c6bd2bf2544\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-a70c2833-8b8f-4aa7-9803-8e05de8dc9a8\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6309148264984227% 0.6309148264984227% 0.6309148264984227% 0.6309148264984227% \/ 3.4482758620689653% 3.4482758620689653% 3.4482758620689653% 3.4482758620689653%\" id=\"el-206d047e-6ce5-42f3-a3d4-c00c67e21a7e\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.4962145110410096% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">Now let us learn some more examples.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.16505%;top:15.37217%;width:76.94175%;height:9.54693%;opacity:1\">\n<div id=\"anim-1374be52-def8-4fbe-9204-9ff5447c1ced\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-443a0ee5-8f03-496b-93bc-009e986f4e52\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6309148264984227% 0.6309148264984227% 0.6309148264984227% 0.6309148264984227% \/ 3.389830508474576% 3.389830508474576% 3.389830508474576% 3.389830508474576%\" id=\"el-8b655310-7d87-4689-9010-b68c60bbfa0d\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.4962145110410096% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">One is with a 3*3 identity matrix:<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:81.22977%;width:76.94175%;height:18.60841%;opacity:1\">\n<div id=\"anim-87a086ca-9157-4e59-8afd-2a5f383bf51d\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-040e6782-0a7f-40c0-b034-85522c55a30f\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6309148264984227% 0.6309148264984227% 0.6309148264984227% 0.6309148264984227% \/ 1.7391304347826086% 1.7391304347826086% 1.7391304347826086% 1.7391304347826086%\" id=\"el-06656428-92dd-40c2-9777-728767a8faf3\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.4736593059936909% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.339806em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">This concludes that every square identity matrix with at least 2 rows and 2 columns is symmetric.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:8.25243%;top:8.57605%;width:80.09709%;height:94.82201%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-67b0a65e-e9a1-4762-bd75-54c702a82fa5\">\n<div style=\"position:absolute;width:100%;height:100.11377%;left:0%;top:-0.05688%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Mathematics-7-1-3.png\" alt=\"Mathematics-7-1 (3)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Mathematics-7-1-3.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Mathematics-7-1-3-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Mathematics-7-1-3-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Mathematics-7-1-3-150x267.png 150w\" sizes=\"(min-width: 1024px) 36vh, 80vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"34fdea89-12c3-41a5-8b71-450eab600902\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-1a2c8e3c-5db7-4838-994c-490acec862bb\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-a8eb116c-2730-4e33-9d9b-dd668051bf81\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-fbb94817-43da-42b6-8797-8e848bb09599\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-8e2f75e8-fc56-4d2a-833d-3008c65906ae\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#fafbfb\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-6f9ff59e-03d9-4797-a1fd-cec8c3fe4869\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/32.jpg\" alt=\"32\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/32.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/32-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/32-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/32-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:3.07443%;width:77.18447%;height:18.60841%;opacity:1\">\n<div id=\"anim-1a2c8e3c-5db7-4838-994c-490acec862bb\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-a8eb116c-2730-4e33-9d9b-dd668051bf81\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.628930817610063% 0.628930817610063% 0.628930817610063% 0.628930817610063% \/ 1.7391304347826086% 1.7391304347826086% 1.7391304347826086% 1.7391304347826086%\" id=\"el-aa912921-41f5-4b2d-abdc-323e511cf0ef\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.47216981132075475% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.339806em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">Now consider a diagonal matrix: i.e., a matrix where all other entries except diagonals are zero.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:80.09709%;width:77.18447%;height:18.60841%;opacity:1\">\n<div id=\"anim-fbb94817-43da-42b6-8797-8e848bb09599\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-8e2f75e8-fc56-4d2a-833d-3008c65906ae\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.628930817610063% 0.628930817610063% 0.628930817610063% 0.628930817610063% \/ 1.7391304347826086% 1.7391304347826086% 1.7391304347826086% 1.7391304347826086%\" id=\"el-db23e9a3-9457-45d6-a097-5d099ac832a9\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.47216981132075475% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.339806em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">This concludes that every square diagonal matrix with at least 2 rows and 2 columns is symmetric.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:0;top:24.43366%;width:80.09709%;height:55.50162%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-0275c0fe-ef10-4881-a01f-bdba8cf1f8a1\">\n<div style=\"position:absolute;width:100%;height:171.03984%;left:0%;top:-35.51992%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-8-1.png\" alt=\"Symmetric matrix-8-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-8-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-8-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-8-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-8-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 36vh, 80vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"a6fc2cea-72d8-475b-aac5-610840aba013\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-a04638c7-550f-472e-9dda-2567bdd117a5\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-f17a8e2d-8d21-4a95-bdce-b7e12b854eb3\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-301f456c-c320-4629-9d03-8f28d40d5ac7\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-ae5f3072-f196-41b3-aaa9-ed66afbfa901\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-f49c3cc3-5c19-4d06-abfe-6f4006cb415e\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-071e8da6-fbfc-41bc-bf8f-9e5b9147600b\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#262626\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-43b4a0aa-5e31-4bf8-aee5-41651d17dcba\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/15.jpg\" alt=\"15\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/15.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/15-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/15-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/15-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:5.82524%;width:77.18447%;height:27.99353%;opacity:1\">\n<div id=\"anim-a04638c7-550f-472e-9dda-2567bdd117a5\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-f17a8e2d-8d21-4a95-bdce-b7e12b854eb3\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.628930817610063% 0.628930817610063% 0.628930817610063% 0.628930817610063% \/ 1.1560693641618496% 1.1560693641618496% 1.1560693641618496% 1.1560693641618496%\" id=\"el-32ab25db-354e-4161-b522-fb3825df7c0d\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.47216981132075475% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.339806em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">a &nbsp;&nbsp; represents the entry of a matrix in the ith row and jth column, \u2018m\u2019 denotes the number of rows and \u2018n\u2019 denotes the number of columns in a matrix, then<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:36.40777%;width:80.09709%;height:57.9288%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-a052680f-62dd-4ff2-a56b-bb626c59c0dc\">\n<div style=\"position:absolute;width:100%;height:163.87338%;left:0%;top:-25.54315%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-9-1-1.png\" alt=\"Symmetric matrix-9-1 (1)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-9-1-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-9-1-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-9-1-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Symmetric-matrix-9-1-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 36vh, 80vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:47.08738%;top:77.83172%;width:77.18447%;height:4.36893%;opacity:1\">\n<div id=\"anim-301f456c-c320-4629-9d03-8f28d40d5ac7\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-ae5f3072-f196-41b3-aaa9-ed66afbfa901\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.628930817610063% 0.628930817610063% 0.628930817610063% 0.628930817610063% \/ 7.4074074074074066% 7.4074074074074066% 7.4074074074074066% 7.4074074074074066%\" id=\"el-88fe8f0c-6630-43f2-8745-4db369e2b047\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.47216981132075475% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.339806em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:13.83495%;top:7.44337%;width:11.8932%;height:3.39806%;opacity:1\">\n<div id=\"anim-f49c3cc3-5c19-4d06-abfe-6f4006cb415e\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-071e8da6-fbfc-41bc-bf8f-9e5b9147600b\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:4.081632653061225% 4.081632653061225% 4.081632653061225% 4.081632653061225% \/ 9.523809523809524% 9.523809523809524% 9.523809523809524% 9.523809523809524%\" id=\"el-e3a6d331-6be2-4093-8358-e6be7d6e0b80\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-2.4806122448979564% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.275081em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">ij<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"8b7df64f-a4e8-4714-a4ff-67d05fd41ccb\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-4e82b4ef-57c7-4d1b-bd98-8391c7fe082b\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-1f94477d-35aa-4b25-a85a-304976f281ab\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#ede7e4\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-c8c11f4d-f05d-41c5-8785-474f680eb2a1\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/share-5.jpg\" alt=\"share-5\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/share-5.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/share-5-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/share-5-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/share-5-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:74.11003%;width:77.18447%;height:24.43366%;opacity:1\">\n<div id=\"anim-4e82b4ef-57c7-4d1b-bd98-8391c7fe082b\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-1f94477d-35aa-4b25-a85a-304976f281ab\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.628930817610063% 0.628930817610063% 0.628930817610063% 0.628930817610063% \/ 1.3245033112582782% 1.3245033112582782% 1.3245033112582782% 1.3245033112582782%\" id=\"el-1d92c7f7-c64d-4bde-96eb-5186e3befd0c\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.49465408805031463% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span>Hope now you are clear about the definition of Symmetric matrix. Share these notes with your friends.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:-3.8835%;top:-9.38511%;width:104.36893%;height:80.90615%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-031dc44d-604b-45fe-9c24-b38cbafa2379\">\n<div style=\"position:absolute;width:162.64803%;height:100%;left:-22.86939%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/Blog-Images-1.jpg\" alt=\"JEECUP 2022 Postponed! UP Polytechnic exam new dates to be announced soon\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><\/amp-story><\/body><\/html><\/p>\n","protected":false},"excerpt":{"rendered":"<p>First  let&#8217;s start with the definition of  \u2018symmetric matrix\u2019  and then we will learn how to check whether a given matrix is symmetric or not.<\/p>\n","protected":false},"author":1,"featured_media":179203,"template":"","meta":{"web_stories_publisher_logo":224678,"web_stories_poster":[],"web_stories_products":[],"footnotes":""},"web_story_category":[2144,2352],"web_story_tag":[3447],"class_list":["post-177544","web-story","type-web-story","status-publish","has-post-thumbnail","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Explained: Symmetric Matrix NCERT Class 12 Maths Chapter 3 Examples<\/title>\n<meta name=\"description\" content=\"Symmetric Matrix Examples: A symmetric matrix is defined as the square matrix that is equal to its transpose matrix. 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