Given $A = \left[ \begin{array} { c c c }
0 & - 2 & - 4 \
6 & 4 & - 2 \
0 & - 8 & - 2
\end{array} \right]$ , find $| A |$ .
A) $168$
B) $40$
C) $- 80$
D) $88$
E) $- 120$

Question

Given $A = \left[ \begin{array} { c c c } 
0 & - 2 & - 4 \
6 & 4 & - 2 \
0 & - 8 & - 2
\end{array} \right]$ , find $| A |$ .
A) $168$
B) $40$
C) $- 80$
D) $88$
E) $- 120$

Quizplus · Accepted Answer

The determinant $|A|$ of matrix $A$ can be calculated using the formula for a 3x3 matrix. Expanding along the first row, we get:$$|A| = 0\cdot\left|\begin{array}{cc}4 & -2 \ -8 & -2\end{array}\right| - (-2)\cdot\left|\begin{array}{cc}6 & -2 \ 0 & -2\end{array}\right| - 4\cdot\left|\begin{array}{cc}6 & 4 \ 0 & -8\end{array}\right|$$$$= 0 - (-2)\cdot(4\cdot(-2) - (-2)\cdot(-8)) - 4\cdot(6\cdot(-8) - 4\cdot0)$$$$= 2\cdot(-8 + 16) - 4\cdot(-48)$$$$= 2\cdot8 + 192$$$$= 16 + 192 = 208$$However, it seems there was a mistake in my calculation as none of the provided options match the result. Let's correct the calculation error:Correctly calculating the determinant:$$|A| = 0\cdot\left|\begin{array}{cc}4 & -2 \ -8 & -2\end{array}\right| - (-2)\cdot\left|\begin{array}{cc}6 & -2 \ 0 & -2\end{array}\right| - 4\cdot\left|\begin{array}{cc}6 & 4 \ 0 & -8\end{array}\right|$$$$= 0 + 2\cdot(6\cdot(-2) - (-2)\cdot0) - 4\cdot(6\cdot(-8) - 4\cdot0)$$$$= 2\cdot(-12) - 4\cdot(-48)$$$$= -24 + 192$$$$= 168$$The correct calculation indeed results in $|A| = 168$, which matches option A.

Given A=[0−2−464−20−8−2]A = \left[ \begin{array} { c c c } 0 & - 2 & - 4 \\6 & 4 & - 2 \\0 & - 8 & - 2\end{array} \right]A=​060​−24−8​−4−2−2​​

Given $A = \left[ \begin{array} { c c c } 0 & - 2 & - 4 \\6 & 4 & - 2 \\0 & - 8 & - 2\end{array} \right]$