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] +1 [-2]

      = 2 [3] - 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
 

adjoint of matrix=

 
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







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