adjoint of a matrix

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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Adjoint of a Matrix

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