Find the determinant of the given matrix.
-$$\left[ \begin{array} { r r r }
- 1 & - 3 & 5 \
- 5 & - 1 & - 5 \
- 4 & 4 & 1
\end{array} \right]$$
A) $- 214$
B) 214
C) $- 104$
D) $- 94$

Question

Find the determinant of the given matrix.
-$$\left[ \begin{array} { r r r } 
- 1 & - 3 & 5 \
- 5 & - 1 & - 5 \
- 4 & 4 & 1
\end{array} \right]$$
A) $- 214$
B) 214
C) $- 104$
D) $- 94$

Quizplus · Accepted Answer

The determinant of a 3x3 matrix $\left[ \begin{array} { r r r } a & b & c \ d & e & f \ g & h & i \end{array} \right]$ is calculated as $a(ei - fh) - b(di - fg) + c(dh - eg)$. Applying this to the given matrix, the determinant is $(-1)((-1)(1) - (-5)(4)) - (-3)((-5)(1) - (-5)(4)) + 5((-5)(4) - (-1)(-5)) = -214$.

Find the Determinant of the Given Matrix [−1−35−5−1−5−441]\left[ \begin{array} { r r r } - 1 & - 3 & 5 \\- 5 & - 1 & - 5 \\- 4 & 4 & 1\end{array} \right]​−1−5−4​−3−14​5−51​​

Find the Determinant of the Given Matrix $\left[ \begin{array} { r r r } - 1 & - 3 & 5 \\- 5 & - 1 & - 5 \\- 4 & 4 & 1\end{array} \right]$