The value of the determinant \(\begin{vmatrix}3 & 0 & 5\\ 2 & 0 & 7\\ 4 & 6 & 1\end{vmatrix}\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(-66\)
The second column has two zeros, so expand along the second column. Only the element 6, in row 3 and column 2, contributes.
\(\displaystyle M_{32} = \begin{vmatrix}3 & 5\\ 2 & 7\end{vmatrix} = 21 - 10 = 11\)
\(A_{32} = (-1)^{3 + 2} \times 11 = -11\)
\(\Delta = 6 \times (-11) = -66\)