Answer to Question #128277 in Linear Algebra for Sym

Question

Find the inverse of the matrix
[ 2 -5 11]
1 1 -6
4 -3 8

Answer 1

To find the inverse

Let consider the given matrix

2 -5 11

1 1 -6 =A(say)

4 -3 8

Let I be the identity matrix of order 3*3

l= 1 0 0

0 1 0

0 0 1

To find the inverse of matrix A we need to apply the formula

A = IA

later it will be like

I=AA(inverse)

Applying following operations

1.R2 interchange with R1

2. R2>R2-2R1

3. R3>R3-4R1

4.R3>R3-R2

5.R2>-R2/7

6.R1>R1-R2

7.R3>R3/9

8.R1>R1-19R3/7

9. R2>R2+23R3/7

By doing several elementary row transformation we get the inverse as

[ -10/63 -32/63 -1/9

1/9 -4/9 1/9

19/63 23/63 1/9]

This is the required answer