Evaluate the determinant $\mid \begin{array} { c c }
e ^ { 7 x } & e ^ { 4 x } \
7 e ^ { 7 x } & 4 e ^ { 4 x }
\end{array}$ 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 $\mid \begin{array} { c c } 
e ^ { 7 x } & e ^ { 4 x } \
7 e ^ { 7 x } & 4 e ^ { 4 x }
\end{array}$ 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

To evaluate the determinant, use the formula for a 2x2 matrix: $ad - bc$, where $a, b, c,$ and $d$ are the elements of the matrix starting from the top left and moving clockwise. Thus, the determinant is $e^{7x} \cdot 4e^{4x} - e^{4x} \cdot 7e^{7x} = 4e^{11x} - 7e^{11x} = -3e^{11x}$.

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

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