Q. 26

Find the value of

Answer :

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,









it is verified that, A(adjA) = (adjA)A = |A|I


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