The value of the determinant \(\begin{vmatrix}2 & 0 & -1\\ 3 & 4 & 0\\ 1 & -2 & 5\end{vmatrix}\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 50
The first row has a zero in the middle, so expanding along the first row needs only two minors.
\( \displaystyle \Delta = 2\begin{vmatrix}4 & 0\\ -2 & 5\end{vmatrix} - 0 + (-1)\begin{vmatrix}3 & 4\\ 1 & -2\end{vmatrix} \)
\( = 2(20 - 0) - 1(-6 - 4) \)
\( = 40 + 10 \)
\( = 50 \)