Inverse of Matrix Questions 4





In this page inverse of matrix questions 4 we are going to see solution of question 4 in the topic inverse of matrix.

Question 4

Find the inverse of the following matrix

 
2 5 7
1 1 1
2 1 -1
 


Solution:

|A|

 = 2

 
1 1

1 -1
 

 -5

 
1 1

2 -1
 

 +7

 
1 1

2 1
 

|A| = 2 [-1-1] - 5 [-1-2] + 7 [1-2]

      = 2 [-2] - 5 [-3] + 7 [-1]

      = -4 + 15 - 7

      = -11 + 15

      = 4

|A| = 4 ≠ 0

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

minor of 2

=
1 1
1 -1

   = [-1-1]

   = (-2)

   = -2

Cofactor of 2

   =  + (-2)

   =    -2

minor of 5

=
1 1
2 -1

inverse of matrix questions 4

   = [-1-2]

   = -3

Cofactor of 5

   =  - (-3)

   =    3

minor of 7

=
1 1
2 1

   = [1-2]

   = -1

Cofactor of 7

   =  + (-1)

   =    -1

minor of 1

=
5 7
1 -1

   = [-5-7]

   = -12

Cofactor of 1

   =  - (-12)

   =    12

minor of 1

=
2 7
2 -1

   = [-2-14]

   = -16

Cofactor of 1

   =  + (-16)

   =   -16

minor of 1

=
2 5
2 1

   = [2-10]

   = -8

Cofactor of 1

   =  - (-8)

   =   8

minor of 2

=
5 7
1 1

   = [5-7]

   = -2

Cofactor of 2

   =  + (-2)

   =   -2

minor of 1

=
2 7
1 1

   = [2-7]

   = -5

Cofactor of 1

   =  - (-5)

   =   5

minor of -1

=
2 5
1 1

   = [2-5]

   = -3

Cofactor of -1

   =  + (-3)

   =   -3

co-factor matrix =

 
-2 3 -1
12 -16 8
-2 5 -3
 

adjoint of matrix=

 
-2 12 -2
3 -16 5
-1 8 -3
 

          A⁻¹ = 1/4

 
-2 12 -2
3 -16 5
-1 8 -3
 









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

5) Find the inverse of the following matrix

 
3 1 -1
2 -1 2
2 1 -2
 

inverse of matrix questions 4

Solution







Inverse of Matrix Question4 to Inverse of a Matrix
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