inverse of matrix questions 5

Inverse of Matrix Questions 5

In this page inverse of matrix questions 5 we are going to see solution of question 5 in the topic inverse of matrix.

Question 5

Find the inverse of the following matrix

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

Solution:

|A|

= 3

-1		2

1		-2

- 1

2		2

2		-2

-1

2		-1

2		1

|A| = 3 [2-2] - 1 [-4-4] - 1 [2-(-2)]

= 3 [0] - 1 [-8] -1 [2+2]

= 3 [0] - 1 [-8] -1 [4]

= 0 + 8 - 4

= 4

|A| = 4 ≠ 0

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

minor of 4

-1	2
1	-2

= [2-2]

= 0

Cofactor of 4

= + (0)

= 0

minor of 1

2	2
2	-2

= [-4-4]

= (-8)

= -8

Cofactor of 1

= - (-8)

= 8

minor of -1

2	-1
2	1

inverse of matrix questions 5 inverse of matrix questions 5

= [2-(-2)]

= (2+2)

= 4

Cofactor of -1

= + (4)

= 4

minor of 2

1	-1
1	-2

= [-2-(-1)]

= (-2+1)

= -1

Cofactor of 2

= - (-1)

= 1

minor of -1

3	-1
2	-2

= [-6-(-2)]

= (-6+2)

= -4

Cofactor of -1

= + (-4)

= -4

minor of 2

3	1
2	1

= [3-2]

= 1

Cofactor of 2

= - (1)

= -1

minor of 2

1	-1
-1	2

= [2-1]

= 1

Cofactor of 2

= + (1)

= 1

minor of 1

3	-1
2	2

= [6-(-2)]

= [6+2]

= 8

Cofactor of 1

= - (8)

= -8

minor of -2

3	1
2	-1

= [-3-2]

= [-5]

= -5

Cofactor of -2

= + (-5)

= -5

co-factor matrix =

0	8	4
1	-4	-1

5	0	-5

adjoint of matrix=

0	1	5
8	-4	0

4	-1	-5

A⁻¹ = 1/4

0	1	5
8	-4	0

4	-1	-5

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

4) Find the inverse of the following matrix

2	5	7
1	1	1
2	1	-1

Solution

HTML Comment Box is loading comments...

SBI!