Evaluate the determinant $$\left | \begin{array} { c c }
e ^ { 7 x } & e ^ { 4 x } \
7 e ^ { 7 x } & 4 e ^ { 4 x }
\end{array} \right |$$ in which the entries are functions.
A) $- 3 e ^ { 11 x }$
B) $\frac { 7 } { 4 } e ^ { 28 x }$
C) $\frac { 4 } { 7 } e ^ { 11 x }$
D) $- 3 e ^ { 28 x }$
E) $- \frac { 3 } { 7 } e ^ { 11 x }$

Question

Evaluate the determinant $$\left | \begin{array} { c c } 
e ^ { 7 x } & e ^ { 4 x } \
7 e ^ { 7 x } & 4 e ^ { 4 x }
\end{array} \right |$$ in which the entries are functions.
A) $- 3 e ^ { 11 x }$
B) $\frac { 7 } { 4 } e ^ { 28 x }$
C) $\frac { 4 } { 7 } e ^ { 11 x }$
D) $- 3 e ^ { 28 x }$
E) $- \frac { 3 } { 7 } e ^ { 11 x }$

Quizplus · Accepted Answer

The determinant of a 2x2 matrix $\left | \begin{array} { c c } a & b \ c & d \end{array} \right |$ is calculated as $ad - bc$. Applying this formula to the given matrix, we get $(e^{7x} \cdot 4e^{4x}) - (7e^{7x} \cdot e^{4x}) = 4e^{11x} - 7e^{11x} = -3e^{11x}$.

Evaluate the Determinant ∣e7xe4x7e7x4e4x∣\left | \begin{array} { c c } e ^ { 7 x } & e ^ { 4 x } \\7 e ^ { 7 x } & 4 e ^ { 4 x }\end{array} \right |​e7x7e7x​e4x4e4x​​

Evaluate the Determinant $\left | \begin{array} { c c } e ^ { 7 x } & e ^ { 4 x } \\7 e ^ { 7 x } & 4 e ^ { 4 x }\end{array} \right |$