Evaluate the determinant.
-$$\left| \begin{array} { l l l l }
0 & 7 & 9 & 7 \
0 & 2 & 9 & 5 \
5 & 4 & 7 & 2 \
4 & 1 & 2 & 2
\end{array} \right|$$
A) 4
B) $- 18$
C) 666
D) $- 31$

Question

Evaluate the determinant.
-$$\left| \begin{array} { l l l l } 
0 & 7 & 9 & 7 \
0 & 2 & 9 & 5 \
5 & 4 & 7 & 2 \
4 & 1 & 2 & 2
\end{array} \right|$$
A) 4
B) $- 18$
C) 666
D) $- 31$

Quizplus · Accepted Answer

The determinant of a 4x4 matrix can be calculated using the method of cofactor expansion. For this particular matrix, it's efficient to expand along the first column because it contains two zeros, which simplifies the calculation. The determinant is thus equal to $5 \cdot C_{31} - 4 \cdot C_{41}$, where $C_{ij}$ denotes the cofactor of the element in the $i$th row and $j$th column. Calculating these cofactors and their corresponding 3x3 determinants, we find the determinant of the original 4x4 matrix to be 666.

Evaluate the Determinant ∣0797029554724122∣\left| \begin{array} { l l l l } 0 & 7 & 9 & 7 \\0 & 2 & 9 & 5 \\5 & 4 & 7 & 2 \\4 & 1 & 2 & 2\end{array} \right|​0054​7241​9972​7522​​

Evaluate the Determinant $\left| \begin{array} { l l l l } 0 & 7 & 9 & 7 \\0 & 2 & 9 & 5 \\5 & 4 & 7 & 2 \\4 & 1 & 2 & 2\end{array} \right|$