Question

find adjoint of matrix

Answer 1

Answer:

Let's write it here to find the adjoint of a we need to find the matrix of the cofactors of each of its elements first. And then take the transpose of that matrix.

Answer 2

Answer:

Let A=[aij] be a square matrix of order n . The adjoint of a matrix A is the transpose of the cofactor matrix of A . It is denoted by adj A . An adjoint matrix is also called an adjugate matrix.

Example:

Find the adjoint of the matrix.

A=⎡⎣⎢321   1−2   2−1   0−1⎤⎦⎥

Step-by-step explanation:

To find the adjoint of a matrix, first find the cofactor matrix of the given matrix. Then find the transpose of the cofactor matrix.

Cofactor of    3= A11=   ∣∣∣−220−1∣∣∣=2

Cofactor of    1= A12=−∣∣∣210−1∣∣∣=2

Cofactor of −1= A13=   ∣∣∣21−22∣∣∣=6

Cofactor of    2= A21=−∣∣∣12−1−1∣∣∣=−1

Cofactor of −2= A22=   ∣∣∣31−1−1∣∣∣=−2

Cofactor of    0= A23=−∣∣∣3112∣∣∣=−5

Cofactor of    1= A31=   ∣∣∣1−2−10∣∣∣=−2

Cofactor of    2= A32=−∣∣∣32−10∣∣∣=−2

Cofactor of −1= A33=   ∣∣∣321−2∣∣∣=−8

The cofactor matrix of A is [Aij]=⎡⎣⎢2−1−22−2−26−5−8⎤⎦⎥

Now find the transpose of Aij .

adj A=(Aij)T             =⎡⎣⎢226−1−2−5−2−2−8⎤⎦⎥

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