Inverse of Matrix Questions 2





In this page inverse of matrix questions 2 we are going to see solution of question 2 in the topic inverse of matrix.

Question 2

Find the inverse of the following matrix

 
1 2 1
2 -1 2
1 1 -2
 


Solution:

|A|

 = 2

 
-1 2

1 -2
 

 -2

 
2 2

1 -2
 

+1

 
2 -1

1 1
 

|A| = 1 [2-2] - 2 [-4-2] +1 [2+1]

      = 1 [0] - 2 [-6] +1 [3]

      = 0 + 12 + 3

      = 15

|A| = 15 ≠ 0

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

minor of 1

=
-1 2
1 -2

   = [2-2]

   = 0

Cofactor of 1

   =  + (0)

   =    0

minor of 2

=
2 2
1 -2

   = [-4-2]

   = -6

Cofactor of 2

   =  - (-6)

   =    6

minor of 1

=
2 -1
1 1

   = [2-(-1)]

   = [2+1]

   = 3

Cofactor of 1

   =  + (3)

   =    3

minor of 2

=
2 1
1 -2

   = [-4-1]

   = -5

Cofactor of 2

   =  - (-5)

   =    5

minor of -1

=
1 1
1 -2

   = [-2-1]

   = -3

Cofactor of -1

   =  + (-3)

   =    -3

minor of 2

=
1 2
1 1

   = [1-2]

   = -1

Cofactor of 2

   =  - (-1)

   =    1

minor of 1

=
2 1
-1 2

   = [4-(-1)]

   = [4+1]

   = 5

Cofactor of 1

   =  + (5)

   =    5

minor of 1

=
1 1
2 2

   = [2-2]

   = [0]

   = 0

Cofactor of 1

   =  - (0)

   =    0

minor of -2

=
1 2
2 -1

   = [-1-4]

   = [-5]

   = -5

Cofactor of -2

   =  + (-5)

   =    -5

inverse of matrix questions 2

co-factor matrix =

 
0 6 3
5 -3 1
5 0 -5
 

adjoint of matrix=

 
0 5 5
6 -3 0
3 1 -5
 

          A⁻¹ = 1/15

 
0 5 5
6 -3 0
3 1 -5
 









Questions



Solution


1) Find the inverse of the following matrix

 
2 1 1
1 1 1
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
 

inverse of matrix questions 2

Solution

5) Find the inverse of the following matrix

 
3 1 -1
2 -1 2
2 1 -2
 

Solution







Inverse of Matrix Question2 to Inverse of a Matrix
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