Adjoint of a Matrix





In this page adjoint of a matrix we are going to some examples to find ad-joint of any matrix.

Definition:

Let A = [aij] be a square matrix of order n. Let Aij be a cofactor of aij. Then nth order matrix [Aij]^T is called adjoint of A. It is denoted by Adj A. In other words we can define adjoint of matrix as transpose of co factor matrix.

Example 1:

Find the adjoint of the following matrix

 
3 4 1
0 -1 2
5 -2 6
 


minor of 3

=
 
-1 2
-2 6
 

   = [-6-(-4)]

   = (-6+4)

   = -2

minor of 4

=
 
0 2
5 6
 

   =  [0-10]

   =  (-10)

   = -10

minor of 1

=
 
0 -1
5 -2
 

   =  [0-(-5)]

   =  [0+5]               minor of a matrix

   =  5

minor of 0

=
 
4 1
-2 6
 

   = [24-(-2)]

   = [24+2]

   =  26

minor of -1

=
 
3 1
5 6
 

   = [18-5]

   =  13

minor of 2

=
 
3 4
5 -2
 

   = [-6-20]

   =  -26

minor of 5

=
 
4 1
-1 2
 

   =  [8-(-1)]

   =  (8+1)

   =  9

minor of -2

=
 
3 1
0 2
 

   =  [6-0]

   =  6

minor of 6

=
 
3 4
0 -1
 

   =  [-3-0]

   =  -3

minor matrix=

 
-2 -10 5
26 13 -26
9 6 -3
 

cofactor matrix =

 
2 10 5
-26 13 26
9 -6 -3
 

adjoint of a matrix =

 
-2 -26 9
10 13 -6
5 26 -3
 







Questions



Solution


1) Find the adjoint of the following matrix

 
2 1 1
1 1 1
1 -1 2
 


Solution

2) Find the adjoint of the following matrix

 
1 2 3
1 1 1
2 3 4
 


Solution

3) Find the adjoint of the following matrix

 
6 2 3
3 1 1
10 3 4
 


Solution

4) Find the adjoint of the following matrix

 
1 1 -1
2 -3 4
3 -2 3
 


Solution

5) Find the adjoint of the following matrix

 
4 2 1
6 3 4
2 1 0
 


Solution

adjoint of a matrix


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