24 Inverse of a Matrix and its Application in Solving System of Linear Equations

Sachin Kumar

Objectives:

1. To find the adjoint of a square matrix
2. To find the inverse of matrix
3. To familiarize the students with use of inverse of matrix for solving system of linear equations

    Introduction

Matrices have applications in various fields. Inverse of matrices also play a vital role. Using inverse of matrix linear system of equations can be solved. Linear systems are also used in modeling real life problems in environmental science. So solution of these linear systems are important which can be found using inverse of matrix. So in this module we will discuss how to find the inverse of a matrix. We will also discuss how to solve linear system of equations using inverse of matrix.

Summery:

In this module, we have introduced the concept of adjoint of matrix and inverse of a matrix. We have shown that a matrix is invertible only if it is non-singular. Then matrix method for solving system of linear equations is introduced. Conditions for consistency and inconsistency of system of linear homogeneous and non-homogeneous systems are also introduced. Various examples have also been discussed to understand the applications of inverse of matrix.

Suggested Books for reading:

[1] Kreyszig, Erwin. Advanced engineering mathematics. John Wiley & Sons, 2010.

[2] Leon, Steven J. Linear algebra with applications. Pearson Prentice Hall, 2006.

[3] Bronson, Richard. Matrix Methods: An Introduction. Academic Press, 1970.

[4] Lay, David C. Linear algebra and its applications, Addison Wesley,