Evaluate.
-$\left| \begin{array} { l l l } 3 & 4 & 6 \ 5 & 3 & 5 \ 1 & 4 & 6 \end{array} \right|$
A) 392
B) $- 44$
C) $- 4$
D) 4

Question

Quizplus · Accepted Answer

We can expand along the first column to get:
$$\left| \begin{array} { l l l } 3 & 4 & 6 \ 5 & 3 & 5 \ 1 & 4 & 6 \end{array} ight| = 3 \left| \begin{array} { l l } 3 & 5 \ 4 & 6 \end{array} ight| - 5 \left| \begin{array} { l l } 4 & 6 \ 4 & 6 \end{array} ight| + 1 \left|\begin{array} { l l } 4 & 5 \ 4 & 3 \end{array} ight| = 3(3\cdot 6 - 5\cdot 4) - 5(4\cdot 6 - 4\cdot 6) + 1(4\cdot 3 - 5\cdot 4) = - 72 + 20 - 4 = \boxed{- 56}.$$

Evaluate - ∣346535146∣\left| \begin{array} { l l l } 3 & 4 & 6 \\ 5 & 3 & 5 \\ 1 & 4 & 6 \end{array} \right|​351​434​656​​

Evaluate
- $\left| \begin{array} { l l l } 3 & 4 & 6 \\ 5 & 3 & 5 \\ 1 & 4 & 6 \end{array} \right|$