Let A = [a ij ] be a square matrix of order 3 × 3 and C ij denote cofactor of a ij in A. If |A| = 5, write the value of a 31 C 31 + a 32 C 32 + a 33 C 33 .

Question

Philoid · Accepted Answer

The value of determinant |A||, of matrix A=[a_ij] of order 3×3, is given to be 5.

The value of determinant written in the form of cofactors is equal to the sum of products of elements of that row (or column) multiplied by their corresponding cofactors.

The value of |A| expanded along row 3 will be

|A|= a₃₁×C₃₁+a₃₂×C₃₂+a₃₃×C₃₃, which is the required expression

Hence, the value of required expression is equal to |A|=5.

Let A = [aij] be a square matrix of order 3 × 3 and Cij denote cofactor of aij in A. If |A| = 5, write the value of a31C31 + a32C32 + a33C33.

Let A = [a_ij] be a square matrix of order 3 × 3 and C_ij denote cofactor of a_ij in A. If |A| = 5, write the value of a₃₁C₃₁ + a₃₂C₃₂ + a₃₃C₃₃.