Question

formula for adjoint A=​

Answer 1

What is the formula of adjoint A?

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 .

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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 .

Step-by-step explanation:

let us understand this with an example

Find the adjoint of the matrix.

A = ⎡ 3 1 -1 ⎤

     ⎢2-2 0 ⎥

     ⎣1    2  −1⎦

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 =   ∣2-0∣ = 2  

Cofactor of    1 = A12 = − ∣-2-0∣ = 2

Cofactor of −1 = A13 =   ∣4-(-2)∣ = 6

Cofactor of    2 = A21=−∣-1-(-2)∣ = −1

Cofactor of −2= A22=   ∣-3+1∣=−2

Cofactor of    0= A23=−∣6-1∣=−5

Cofactor of    1= A31=   ∣0-2∣=−2

Cofactor of    2= A32=−∣0=2∣=−2

Cofactor of −1= A33=   ∣-6-2∣=−8

The cofactor matrix of A is [Aij]=⎡ 2  2  6⎤

                                                     ⎢-1 -2 -5⎥

                                                     ⎣-2 -2-8⎦

Now find the transpose of Aij .

adj A=(Aij)T        

           = ⎡2 -1-2⎤

           ⎢2-2 -2⎥  

           ⎣6 -5-8⎦