## Inverse of Matrix Questions 1

In this page inverse of matrix questions 1 we are going to see solution of question 1 in the topic inverse of matrix.

Question 1

Find the inverse of the following matrix

 2 1 1 1 1 1 1 -1 2

Solution:

= 2

 1 1 -1 2

- 1

 1 1 1 2

+ 1

 1 1 1 -1

|A| = 2 [2-(-1)] - 1 [2-1] +1 [-1-1]

= 2 [2+1] - 1  +1 [-2]

= 2  - 1 -2

= 6 - 3

= 3

|A| = 3 ≠ 0

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

minor of 2

=
 1 1 -1 2

= [2-(-1)]

= (2+1)

= 3

Cofactor of 2

=  + (3)

=    3

minor of 1

=
 1 1 1 2

= [2-1]

= 1

Cofactor of 1

=  -(1)

=  -1

minor of 1

=
 1 1 1 -1

= [-1-1]

= -2

Cofactor of 1

=  + (-2)

=  -2

minor of 1

=
 1 1 -1 2

= [2-(-1)]

= [2+1]

= 3

Cofactor of 1

=  - (3)

=  -3

minor of 1

=
 2 1 1 2

= [4-1]

= 3

= 3

Cofactor of 1

=  + (3)

=  3

minor of 1

=
 2 1 1 -1

= [-2-1]

= -3

= -3

Cofactor of 1

=  - (-3)

=  3

minor of 1

=
 1 1 1 1

= [1-1]

= 0

Cofactor of 1

=  + (0)

=  0

minor of -1

=
 2 1 1 1

= [2-1]

= 1

Cofactor of -1

=  - (1)

=  -1

minor of 2

=
 2 1 1 1

= [2-1]

= 1

Cofactor of 2

=  + (1)

=  1

inverse of matrix questions 1

co-factor matrix =

 3 -1 -2 -3 3 3 0 -1 1

 3 -3 0 -1 3 -1 -2 3 1

A⁻¹ = 1/3

 3 -3 0 -1 3 -1 -2 3 1

Questions

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

4) Find the inverse of the following matrix

 2 5 7 1 1 1 2 1 -1

Solution

5) Find the inverse of the following matrix

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

inverse of matrix questions 1

Solution  