Find the determinant of $$\left[ \begin{array} { c c c }
6 & - 2 & 0 \
- 4 & 4 & 0 \
2 & 16 & 2
\end{array} \right]$$ .
A)32
B)0
C)24
D)-56
E)-64

Question

Find the determinant of $$\left[ \begin{array} { c c c } 
6 & - 2 & 0 \
- 4 & 4 & 0 \
2 & 16 & 2
\end{array} \right]$$ .
A)32
B)0
C)24
D)-56
E)-64

Quizplus · Accepted Answer

The determinant of a 3x3 matrix $\left[ \begin{array} { c c c } a & b & c \ d & e & f \ g & h & i \end{array} \right]$ is calculated as $a(ei - fh) - b(di - fg) + c(dh - eg)$. Applying this formula to the given matrix, we get $6(4*2 - 0*16) - (-2)(-4*2 - 0*2) + 0(-4*16 - (-4)*16) = 6(8) - (-2)(-8) + 0 = 48 - 16 = 32$.

Find the Determinant Of [6−20−4402162]\left[ \begin{array} { c c c } 6 & - 2 & 0 \\- 4 & 4 & 0 \\2 & 16 & 2\end{array} \right]​6−42​−2416​002​​

Find the Determinant Of $\left[ \begin{array} { c c c } 6 & - 2 & 0 \\- 4 & 4 & 0 \\2 & 16 & 2\end{array} \right]$