Question

If C_ij is the cofactor of the element a_ij of the matrix $A=\left[\begin{array}{ccc}2& -3& 5\\ 6& 0& 4\\ 1& 5& -7\end{array}\right]$, then write the value of a₃₂C₃₂.

Answer 1

In the given matrix $A=\left[\begin{array}{ccc}2& -3& 5\\ 6& 0& 4\\ 1& 5& -7\end{array}\right]$,
C₃₂ = (−1)^{3 + 2} (8 − 30) = 22

Therefore, a₃₂C₃₂ = 5 × 22 = 110.

Hence, the value of a₃₂C₃₂ is 110.