Evaluate the determinant of the matrix below. $\left[ \begin{array} { c c c c }
1 & 4 & 6 & - 7 \
0 & - 4 & - 4 & - 1 \
0 & 0 & - 3 & - 6 \
0 & 0 & 0 & 5
\end{array} \right]$
A)-9
B)1
C)-1
D)60
E)32

Question

Evaluate the determinant of the matrix below. $\left[ \begin{array} { c c c c } 
1 & 4 & 6 & - 7 \
0 & - 4 & - 4 & - 1 \
0 & 0 & - 3 & - 6 \
0 & 0 & 0 & 5
\end{array} \right]$
A)-9
B)1
C)-1
D)60
E)32

Quizplus · Accepted Answer

The determinant of a triangular matrix (either upper or lower triangular) is the product of its diagonal elements. Thus, the determinant is $1 \times (-4) \times (-3) \times 5 = 60$.

Evaluate the Determinant of the Matrix Below [146−70−4−4−100−3−60005]\left[ \begin{array} { c c c c } 1 & 4 & 6 & - 7 \\0 & - 4 & - 4 & - 1 \\0 & 0 & - 3 & - 6 \\0 & 0 & 0 & 5\end{array} \right]​1000​4−400​6−4−30​−7−1−65​​

Evaluate the Determinant of the Matrix Below $\left[ \begin{array} { c c c c } 1 & 4 & 6 & - 7 \\0 & - 4 & - 4 & - 1 \\0 & 0 & - 3 & - 6 \\0 & 0 & 0 & 5\end{array} \right]$