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)-80
C)-88
D)40
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)-80
C)-88
D)40
E)120

Quizplus · Accepted Answer

To find the determinant $|A|$ of matrix $A$, we can use the method of cofactor expansion. Expanding along the first row, we get:$$|A| = 0\cdot\left|\begin{array}{cc}-4 & 2 \ 8 & 2\end{array}\right| - 2\cdot\left|\begin{array}{cc}-6 & 2 \ 0 & 2\end{array}\right| + 4\cdot\left|\begin{array}{cc}-6 & -4 \ 0 & 8\end{array}\right|$$$$= 0 - 2((-6)(2) - (0)(2)) + 4((-6)(8) - (-4)(0))$$$$= 0 - 2(-12) + 4(-48)$$$$= 24 - 192$$$$= -168$$

Given A=[024−6−42082]A = \left[ \begin{array} { c c c } 0 & 2 & 4 \\- 6 & - 4 & 2 \\0 & 8 & 2\end{array} \right]A=​0−60​2−48​422​​

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