Algebra of matrices is a term in mathematics, which deals with the vector spaces between different dimensions. The innovation of matrix algebra indeed came into existence because of n-dimensional planes present in our coordinate space. The RD Sharma Solutions for Class 12 Maths Chapter 5 algebra of matrices involves matrices, namely Addition, Subtraction, Multiplication and Division.
Furthermore, students also get an eye on another important topic called types of matrix. The following are the different types of matrices: row matrix, column matrix, Zero to Null matrix, Horizontal matrix, Vertical matrix, Singleton matrix, Square matrix, Diagonal matrix, Scalar matrix, Equal matrix, identity (unit) matrix, Equal matrix, Triangular matrix, Singular matrix, Non-Singular matrix, Symmetric matrices, Skew-Symmetric matrices, Hermitian matrix, Skew-Hermitian matrix, Orthogonal matrix, Idempotent matrix, Involuntary matrix, Nilpotent matrix
In this chapter, a concept named Equality of matrices is also being discussed. Two matrices are equal if they have the same dimension or order and the corresponding elements are identical. Apart from this, they are also taught the topic called Matrix addition and its properties which can be very useful while solving the problems based on this concept.
Moreover, students learn another important topic called multiplication of a matrix by a scalar. After mastering this concept, they get exposed to a topic called Properties of scalar multiplication. Other related topics such as Subtraction of matrices and Multiplication of matrices are also being taught intensively, and exercise problems are solved in the solutions provided. Properties of matrix multiplication are also a fundamental topic where students can use it to arrive at the correct results.
Other than all this, few more related topics, namely Transpose of a matrix and Properties of transpose, are also being discussed where students gain a whole new idea and enhance their knowledge by practising related problems.