Evaluate Higher-Order Determinants
-$$\left| \begin{array} { l l l l }
0 & 0 & 0 & 8 \
4 & 6 & 9 & 5 \
9 & 8 & 7 & 3 \
3 & 3 & 1 & 7
\end{array} \right|$$
A) $- 376$
B) 376
C) $- 56$
D) $- 8$

Question

Evaluate Higher-Order Determinants
-$$\left| \begin{array} { l l l l } 
0 & 0 & 0 & 8 \
4 & 6 & 9 & 5 \
9 & 8 & 7 & 3 \
3 & 3 & 1 & 7
\end{array} \right|$$
A) $- 376$
B) 376
C) $- 56$
D) $- 8$

Quizplus · Accepted Answer

The determinant of a matrix can be calculated using the Laplace expansion, which involves expanding the determinant across a row or column. In this case, choosing the first row for expansion is most efficient because it contains three zeros, simplifying the calculation. The determinant then becomes the value of the element in the first row and fourth column (8) multiplied by the determinant of the 3x3 matrix that remains after removing the first row and fourth column, with a sign determined by the position (i+j, where i and j are the row and column indices of the element, respectively). The calculation yields -376.

Evaluate Higher-Order Determinants - ∣0008469598733317∣\left| \begin{array} { l l l l } 0 & 0 & 0 & 8 \\4 & 6 & 9 & 5 \\9 & 8 & 7 & 3 \\3 & 3 & 1 & 7\end{array} \right|​0493​0683​0971​8537​​

Evaluate Higher-Order Determinants
- $\left| \begin{array} { l l l l } 0 & 0 & 0 & 8 \\4 & 6 & 9 & 5 \\9 & 8 & 7 & 3 \\3 & 3 & 1 & 7\end{array} \right|$