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

 -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

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 1. Click on the HTML link code below.

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