## Inverse of Matrix Questions 4

In this page inverse of matrix questions 4 we are going to see solution of question 4 in the topic inverse of matrix.

Question 4

Find the inverse of the following matrix

 2 5 7 1 1 1 2 1 -1

Solution: |A|

= 2

 1 1 1 -1

-5

 1 1 2 -1

+7

 1 1 2 1

|A| = 2 [-1-1] - 5 [-1-2] + 7 [1-2]

= 2 [-2] - 5 [-3] + 7 [-1]

= -4 + 15 - 7

= -11 + 15

= 4

|A| = 4 ≠ 0

Since A is a non singular matrix. A⁻¹ exists.

minor of 2

=
 1 1 1 -1

= [-1-1]

= (-2)

= -2

Cofactor of 2

=  + (-2)

=    -2

minor of 5

=
 1 1 2 -1

inverse of matrix questions 4

= [-1-2]

= -3

Cofactor of 5

=  - (-3)

=    3

minor of 7

=
 1 1 2 1

= [1-2]

= -1

Cofactor of 7

=  + (-1)

=    -1

minor of 1

=
 5 7 1 -1

= [-5-7]

= -12

Cofactor of 1

=  - (-12)

=    12

minor of 1

=
 2 7 2 -1

= [-2-14]

= -16

Cofactor of 1

=  + (-16)

=   -16

minor of 1

=
 2 5 2 1

= [2-10]

= -8

Cofactor of 1

=  - (-8)

=   8

minor of 2

=
 5 7 1 1

= [5-7]

= -2

Cofactor of 2

=  + (-2)

=   -2

minor of 1

=
 2 7 1 1

= [2-7]

= -5

Cofactor of 1

=  - (-5)

=   5

minor of -1

=
 2 5 1 1

= [2-5]

= -3

Cofactor of -1

=  + (-3)

=   -3

co-factor matrix =

 -2 3 -1 12 -16 8 -2 5 -3

 -2 12 -2 3 -16 5 -1 8 -3

A⁻¹ = 1/4

 -2 12 -2 3 -16 5 -1 8 -3

Questions

Solution

1) Find the inverse of the following matrix

 2 1 1 1 1 1 1 -1 2

Solution

2) Find the inverse of the following matrix

 1 2 1 2 -1 2 1 1 -2

Solution

3) Find the inverse of the following matrix

 6 2 3 3 1 1 10 3 4

Solution

5) Find the inverse of the following matrix

 3 1 -1 2 -1 2 2 1 -2

inverse of matrix questions 4

Solution Inverse of Matrix Question4 to Inverse of a Matrix 