Use the matrix capabilities of a graphing utility to find the determinant of the matrix $$\left[ \begin{array} { l l l l l }
2 & 0 & 0 & 0 & 0 \
0 & - 4 & 0 & 0 & 0 \
0 & 0 & 6 & 0 & 0 \
0 & 0 & 0 & - 2 & 0 \
0 & 0 & 0 & 0 & 4
\end{array} \right]$$ .
A) $48$
B) $64$
C) $32$
D) $384$
E) $- 128$

Question

Use the matrix capabilities of a graphing utility to find the determinant of the matrix $$\left[ \begin{array} { l l l l l } 
2 & 0 & 0 & 0 & 0 \
0 & - 4 & 0 & 0 & 0 \
0 & 0 & 6 & 0 & 0 \
0 & 0 & 0 & - 2 & 0 \
0 & 0 & 0 & 0 & 4
\end{array} \right]$$ .
A) $48$
B) $64$
C) $32$
D) $384$
E) $- 128$

Quizplus · Accepted Answer

The determinant of a diagonal matrix (where all off-diagonal elements are zero) is the product of its diagonal elements. Thus, the determinant is $2 \times -4 \times 6 \times -2 \times 4 = 384$.

Use the Matrix Capabilities of a Graphing Utility to Find