Find the determinant of the given matrix.
-$$\left[ \begin{array} { l l l l }
7 & 5 & 4 & 9 \
2 & 5 & 7 & 3 \
5 & 7 & 9 & 2 \
3 & 7 & 7 & 6
\end{array} \right]$$
A) $- 51$
B) $- 304$
C) $- 73$
D) $- 39$

Question

Find the determinant of the given matrix.
-$$\left[ \begin{array} { l l l l } 
7 & 5 & 4 & 9 \
2 & 5 & 7 & 3 \
5 & 7 & 9 & 2 \
3 & 7 & 7 & 6
\end{array} \right]$$
A) $- 51$
B) $- 304$
C) $- 73$
D) $- 39$

Quizplus · Accepted Answer

The determinant of a 4x4 matrix can be calculated using the Laplace expansion, which involves expanding the determinant across a row or column and calculating the determinants of the resulting 3x3 matrices. This process is tedious to perform manually for each option without specific computational tools or software. However, given the options, the correct determinant of the given matrix is $-304$, which can be verified using a matrix calculator or appropriate software designed for linear algebra computations.

Find the Determinant of the Given Matrix [7549257357923776]\left[ \begin{array} { l l l l } 7 & 5 & 4 & 9 \\2 & 5 & 7 & 3 \\5 & 7 & 9 & 2 \\3 & 7 & 7 & 6\end{array} \right]​7253​5577​4797​9326​​

Find the Determinant of the Given Matrix $\left[ \begin{array} { l l l l } 7 & 5 & 4 & 9 \\2 & 5 & 7 & 3 \\5 & 7 & 9 & 2 \\3 & 7 & 7 & 6\end{array} \right]$