TCO 6 Explain what an inverse matrix is and how it can be us

(TCO 6) Explain what an inverse matrix is and how it can be used to solve a system of equations.

Solution

Definition of Inverse matrix:

Let \'A\' be a square matrix of order nxn. Then a square matrix \'B\' of same order is said be inverse of A if and only if,

AB = BA = I, where \'I\' is an identity matrix of the same order nxn. The inverse of \'A\' is usually denoted by A^-1.

i.e., B = A^-1.

Then we get AA^-1=A^-1A=I.

How inverse matrix is used to solve system of equations?:

Let Ax = B be any system of equations.

Let us multiply both sides by A^-1 on left side, then we get

A^-1 (Ax) = A^-1B

(A^-1A) x = A^-1B

Ix = A^-1B

x = A^-1B, which is the solution of the given system.

(It means for finding the solution of the given system, we just have to find A^-1 first and then multiply A^-1 by B to get the solution \'x\')