Q2 of 74 Page 7

Find the adjoint of each of the following Matrices and Verify that (adj A) A = |A| I = A (adj A)


Verify that (adj A) A=|A| I=A (adj A) for the above matrices.

A =


Cofactors of A


C11 = – 22 C21 = 11 C31 = – 11


C12 = 4 C22 = – 2 C32 = 2


C13 = 16 C23 = – 8 C33 = 8


adj A =


=


adj A =


Now, (adj A).A =


=


=


Also, |A|.I =


= [2( – 2 – 20) + 1( – 4 – 0) + 3(16 – 0)]


= ( – 44 – 4 + 48)


=


Then, A.(adj A) =


=


=


Hence, (adj A).A = |A|.I = A(adj A)


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2

Find the adjoint of each of the following Matrices and Verify that (adj A) A = |A| I = A (adj A)


Verify that (adj A) A=|A| I=A (adj A) for the above matrices.

 2

Find the adjoint of each of the following Matrices and Verify that (adj A) A = |A| I = A (adj A)


Verify that (adj A) A=|A| I=A (adj A) for the above matrices.

 2

Find the adjoint of each of the following Matrices and Verify that (adj A) A = |A| I = A (adj A)


Verify that (adj A) A=|A| I=A (adj A) for the above matrices.

 3

For the matrix A= , show that A(adj A)=O.