question_answer 1)

Using cofactors of elements of third column, evaluate  

Answer:

Cofactor of element yz = A13       = (?1)1+3             Cofactor of element zx = A23             Cofactor of element xy = A33                                          As we know that        sum of the product of elements of any row (or column) with their corresponding cofactors       yz (z ? y) + zx (x ? z) + xy (y ? x)       = yz2 ? zy2 + zx2 ? xz2 + xy2 ? yx2       = xyz ? zx2 + xz2 ? xz2 ? zy2 + xy2 + yz2 ? xyz       = x(yz ? xy ? z2 + zx) ? y (yz ? xy ? z2 + zx)       = (x ? y) (yz ? xy ?z2 + zx)       = (x ? y) (y (z ? x) ? z(z ? x))       = (x ? y) (y ? z) (z ? x)