Evaluate.
-$$\left| \begin{array} { r r r }
- 1 & 2 & 5 \
3 & - 1 & - 5 \
5 & - 1 & - 4
\end{array} \right|$$
A) $- 15$
B) 85
C) $- 123$
D) 15

Question

Evaluate.
-$$\left| \begin{array} { r r r } 
- 1 & 2 & 5 \
3 & - 1 & - 5 \
5 & - 1 & - 4
\end{array} \right|$$
A) $- 15$
B) 85
C) $- 123$
D) 15

Quizplus · Accepted Answer

The determinant is evaluated as follows:$$\left| \begin{array} { r r r } - 1 & 2 & 5 \3 & - 1 & - 5 \5 & - 1 & - 4\end{array} ight| = -1\left| \begin{array} { r r } - 1 & - 5 \- 1 & - 4\end{array} ight| - 2\left| \begin{array} { r r } 3 & - 5 \5 & - 4\end{array} ight| + 5\left| \begin{array} { r r } 3 & - 1 \5 & - 1\end{array} ight|$$$$= -1(4 - 5) - 2(-12 - (-25)) + 5(-3 - (-5))$$$$= -1(-1) - 2(13) + 5(2)$$$$= 1 - 26 + 10 = -15$$

Evaluate - ∣−1253−1−55−1−4∣\left| \begin{array} { r r r } - 1 & 2 & 5 \\3 & - 1 & - 5 \\5 & - 1 & - 4\end{array} \right|​−135​2−1−1​5−5−4​​

Evaluate
- $\left| \begin{array} { r r r } - 1 & 2 & 5 \\3 & - 1 & - 5 \\5 & - 1 & - 4\end{array} \right|$