Find the value of the determinant.
-$$\left| \begin{array} { r r r }
1 & 5 & - 4 \
- 5 & 1 & 1 \
4 & - 4 & - 2
\end{array} \right|$$
A) $- 32$
B) $- 92$
C) $- 132$
D) 92

Question

Find the value of the determinant.
-$$\left| \begin{array} { r r r } 
1 & 5 & - 4 \
- 5 & 1 & 1 \
4 & - 4 & - 2
\end{array} \right|$$
A) $- 32$
B) $- 92$
C) $- 132$
D) 92

Quizplus · Accepted Answer

The determinant of a 3x3 matrix $\begin{vmatrix} a & b & c \ d & e & f \ g & h & i \end{vmatrix}$ is calculated as $a(ei - fh) - b(di - fg) + c(dh - eg)$. Applying this formula to the given matrix, we get $1(1 \cdot -2 - 1 \cdot -4) - 5(-5 \cdot -2 - 1 \cdot 4) + (-4)(-5 \cdot -4 - 1 \cdot 4)$, which simplifies to $-92$.

Find the Value of the Determinant ∣15−4−5114−4−2∣\left| \begin{array} { r r r } 1 & 5 & - 4 \\- 5 & 1 & 1 \\4 & - 4 & - 2\end{array} \right|​1−54​51−4​−41−2​​

Find the Value of the Determinant $\left| \begin{array} { r r r } 1 & 5 & - 4 \\- 5 & 1 & 1 \\4 & - 4 & - 2\end{array} \right|$