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

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) $6 + 16 u v$
B) $6 u v + 16$
C) $6 u v - 16$
D) $6 - 16 u v$
E) $6 - u v$

Quizplus · Accepted Answer

The determinant of a 2x2 matrix $\left| \begin{array} { c c } a & b \ c & d \end{array} \right|$ is calculated as $ad - bc$. For the given matrix, $a = 2u$, $b = -4$, $c = -4$, and $d = 3v$. Thus, the determinant is $(2u)(3v) - (-4)(-4) = 6uv - 16$.

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 $\left| \begin{array} { c c } 2 u & - 4 \\- 4 & 3 v\end{array} \right|$