Q. 26

# Find the value of

A’ (Transpose of A) is defined by

If A = [aij]m × n then A’ = [aji]n × m

Therefore, we have

A’ = A

Comparing corresponding elements, we have

x = 2y

x = z

y = z

Therefore, general solution will be

x = 2z, y = z, z = z

[Infinitely many solutions possible]

OR

We know,

Minor of an element aij of the determinant of matrix A is the determinant obtained by deleting ith row and jth column and denoted by Mij

and

Cofactor of aij of given by Aij = (– 1)i+j Mij

And

Value of determinant of a matrix A is obtained by

|A| = a11A11 + a12A12 + a13A13

And

If then,

where, Aij is cofactor of aij

Calculating for

We get,

a11 = 1, A11 = 0

a12 = -1, A12 = -11

a13 = 2, A13 = 0

a21 = 3, A21 = 3

a22 = 0, A22 = 1

a23 = -2, A23 = -1

a31 = 1, A31 = 2

a32 = 3, A32 = 8

a33 = 3, A33 = 3

|A| = 1(0) + (-1) (-11) + 2(0) = 11

Now,

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