Evaluate.
-$$\left| \begin{array} { r r r }
- 1 & - 3 & 4 \
- 4 & - 3 & - 3 \
1 & - 3 & - 5
\end{array} \right|$$
A) $- 123$
B) 123
C) $- 39$
D) 105

Question

Evaluate.
-$$\left| \begin{array} { r r r } 
- 1 & - 3 & 4 \
- 4 & - 3 & - 3 \
1 & - 3 & - 5
\end{array} \right|$$
A) $- 123$
B) 123
C) $- 39$
D) 105

Quizplus · Accepted Answer

Explanation:Using the first column as the pivot column, we can expand the determinant as follows:$$\left| \begin{array} { r r r } - 1 & - 3 & 4 \- 4 & - 3 & - 3 \1 & - 3 & - 5\end{array} ight| = -1 \left| \begin{array} { r r } - 3 & - 3 \- 3 & - 5\end{array} ight| - (-3) \left| \begin{array} { r r } - 4 & - 3 \1 & - 5\end{array} ight| + 4 \left| \begin{array} { r r } - 4 & - 3 \1 & - 3\end{array} ight|$$$$= -1 [(15 - 9)] - (-3)[(-20) - (-3)] + 4[(12) - (-3)]$$$$= -1 (6) - (-3)(-17) + 4(15)$$$$= -6 + 51 + 60$$$$= 123$$

Evaluate - ∣−1−34−4−3−31−3−5∣\left| \begin{array} { r r r } - 1 & - 3 & 4 \\- 4 & - 3 & - 3 \\1 & - 3 & - 5\end{array} \right|​−1−41​−3−3−3​4−3−5​​

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