The value of the determinant \(\begin{vmatrix}3 & -1 & 2\\ 0 & 4 & 1\\ 2 & 1 & -3\end{vmatrix}\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(-57\)
Let us expand along the first row, with the signs \(+,\ -,\ +\):
\(\Delta = 3\big(4 \cdot (-3) - 1 \cdot 1\big) - (-1)\big(0 \cdot (-3) - 1 \cdot 2\big) + 2\big(0 \cdot 1 - 4 \cdot 2\big)\)
\(\Delta = 3(-13) + 1(-2) + 2(-8)\)
\(\Delta = -39 - 2 - 16\)
\(\Delta = -57\)