On expanding by first row, the value of the determinant of 3 × 3 square matrix A = [a_ij] is a₁₁C₁₁ + a₁₂C₁₂ + a₁₃C₁₃, where C_ij is the cofactor of a_ij is the cofactor of a_ij in A. Write the expression for its value of expanding by second column.

Question

On expanding by first row, the value of the determinant of 3 × 3 square matrix A = [a_ij] is a₁₁C₁₁ + a₁₂C₁₂ + a₁₃C₁₃, where C_ij is the cofactor of a_ij is the cofactor of a_ij in A. Write the expression for its value of expanding by second column.

Philoid · Accepted Answer

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.

Hence, the value of determinant |A|, of matrix A=[a_ij] of order 3×3, expanded along column 2 will be

|A|=a₁₂×C₁₂+a₂₂×C₂₂+a₃₂×C₃₂

On expanding by first row, the value of the determinant of 3 × 3 square matrix A = [aij] is a11C11 + a12C12 + a13C13, where Cij is the cofactor of aij is the cofactor of aij in A. Write the expression for its value of expanding by second column.

On expanding by first row, the value of the determinant of 3 × 3 square matrix A = [a_ij] is a₁₁C₁₁ + a₁₂C₁₂ + a₁₃C₁₃, where C_ij is the cofactor of a_ij is the cofactor of a_ij in A. Write the expression for its value of expanding by second column.