Evaluate the determinant in which the entries are functions. $$\left| \begin{array} { c c }
2 u & - 4 \
- 4 & 3 v
\end{array} \right|$$
A) $6 + 16 \text{uv}$
B) $6 \text{uv} + 16$
C) $6 \text{uv} - 16$
D) $6 - 16 \text{uv}$
E) $6 - \text{uv}$

Question

Evaluate the determinant in which the entries are functions.​ $$\left| \begin{array} { c c } 
2 u & - 4 \
- 4 & 3 v
\end{array} \right|$$ ​
A) $6 + 16 \text{uv}$
B) $6 \text{uv} + 16$
C) $6 \text{uv} - 16$
D) $6 - 16 \text{uv}$
E) $6 - \text{uv}$

Quizplus · Accepted Answer

Using row operations, we can simplify the determinant to:
$$\begin{vmatrix}1 & 2 & 3 \ 2 & 3 & 4 \ 3 & 4 & 5\end{vmatrix} = \begin{vmatrix}1 & 2 & 3 \ -2 & -1 & -2 \ 0 & 2 & 2\end{vmatrix} = \begin{vmatrix}-1 & -2 \ 2 & 2\end{vmatrix} = -6$$
Hence, the correct choice is C since it has a determinant equal to -6.

Evaluate the Determinant in Which the Entries Are Functions ∣2u−4−43v∣\left| \begin{array} { c c } 2 u & - 4 \\- 4 & 3 v\end{array} \right|​2u−4​−43v​​

Evaluate the Determinant in Which the Entries Are Functions $\left| \begin{array} { c c } 2 u & - 4 \\- 4 & 3 v\end{array} \right|$