Students understand a consistent system in RD Sharma Solutions for Class 12th Maths Chapter 8 solutions of simultaneous equations. A consistent system is nothing but a system with at least one solution, and it is said to be independent if it has exactly one solution. If a consistent system has an infinite number of solutions, then it is called dependent. When you try to make a graph of those equations, they both represent the same line.
Secondly, students get an eye on homogeneous and non-homogeneous systems. A homogeneous system is one in which all of the constant terms are zero, and they always have at least one solution named a zero vector. On the other hand, a non-homogeneous system has an associated homogeneous function, which you obtain by replacing the constant term in each equation with zero.
After understanding the topics mentioned above, students are taught a topic called the matrix method for the solution of a non-homogeneous system. Additionally, they also learn how to solve the given system of linear equations when the coefficient matrix is non-singular and solve the provided set of equations when the coefficient matrix is singular.
Moreover, students learn how to solve linear equations when the inverse of the coefficient matrix is attained. Apart from all of them, they also are educated on the applications of simultaneous linear equations.
Furthermore, students learn how to solve the homogeneous system of linear equations when the determinant of the coefficient matrix is nonsingular. The solution of the homogeneous system of linear equations when the determinant of the coefficient matrix is singular is also covered by the chapter. Thus, students learn the concepts and are exposed to practice problems that are given after every topic.