Inverse of Matrix Questions 5





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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

   = -1

Cofactor of 2

   =  - (-1)

   =    1

minor of -1

=
3 -1
2 -2

   = [-6-(-2)]

   = (-6+2)

   = -4

   = -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







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