Evaluate a Third-Order Determinant
-$$\left| \begin{array} { r r r }
- 4 & 3 & 3 \
2 & 0 & 1 \
- 5 & 0 & - 1
\end{array} \right|$$
A) $- 9$
B) $- 21$
C) 9
D) 21

Question

Evaluate a Third-Order Determinant
-$$\left| \begin{array} { r r r } 
- 4 & 3 & 3 \
2 & 0 & 1 \
- 5 & 0 & - 1
\end{array} \right|$$
A) $- 9$
B) $- 21$
C) 9
D) 21

Quizplus · Accepted Answer

The determinant can be evaluated as follows:$$\left| \begin{array} { r r r } - 4 & 3 & 3 \2 & 0 & 1 \- 5 & 0 & - 1\end{array} ight| = -4\left| \begin{array} { r r } 0 & 1 \0 & - 1\end{array} ight| - 3\left| \begin{array} { r r } 2 & 1 \- 5 & - 1\end{array} ight| + 3\left| \begin{array} { r r } 2 & 0 \- 5 & 0\end{array} ight|$$$$= -4(0) - 3(-2 - 5) + 3(0) = -3(-7) = 21$$

Evaluate a Third-Order Determinant - ∣−433201−50−1∣\left| \begin{array} { r r r } - 4 & 3 & 3 \\2 & 0 & 1 \\- 5 & 0 & - 1\end{array} \right|​−42−5​300​31−1​​

Evaluate a Third-Order Determinant
- $\left| \begin{array} { r r r } - 4 & 3 & 3 \\2 & 0 & 1 \\- 5 & 0 & - 1\end{array} \right|$