Compute the determinant of the matrix by cofactor expansion.
-$$\left[ \begin{array} { r r r r r }
2 & 2 & - 2 & 5 & - 4 \
0 & 3 & 2 & 1 & 0 \
0 & 0 & - 2 & 3 & 7 \
0 & 0 & 0 & - 1 & - 5 \
0 & 0 & 0 & 0 & 2
\end{array} \right]$$
A) 24
B) $- 24$
C) $- 12$
D) 0

Question

Compute the determinant of the matrix by cofactor expansion.
-$$\left[ \begin{array} { r r r r r } 
2 & 2 & - 2 & 5 & - 4 \
0 & 3 & 2 & 1 & 0 \
0 & 0 & - 2 & 3 & 7 \
0 & 0 & 0 & - 1 & - 5 \
0 & 0 & 0 & 0 & 2
\end{array} \right]$$
A) 24
B) $- 24$
C) $- 12$
D) 0

Quizplus · Accepted Answer

The determinant of a triangular matrix (all zeros below or above the main diagonal) is the product of its diagonal elements. Thus, the determinant is $2 \times 3 \times (-2) \times (-1) \times 2 = 24$.

Compute the Determinant of the Matrix by Cofactor Expansion A) 24 B)

Compute the Determinant of the Matrix by Cofactor Expansion A) 24
B)