Choose the one alternative that best completes the statement or answers the question.
Evaluate the determinant of the given matrix.
-$$A = \left[ \begin{array} { c c }
e ^ { x } & e ^ { 9 x } \
6 & - e ^ { 8 x }
\end{array} \right]$$
A) $- 7 e ^ { 9 x }$
B) $- e ^ { 8 x } - 6 e ^ { 9 x }$
C) $- 5 e ^ { 9 x }$
D) $7 e ^ { 9 x }$

Question

Choose the one alternative that best completes the statement or answers the question.
Evaluate the determinant of the given matrix.
-$$A = \left[ \begin{array} { c c } 
e ^ { x } & e ^ { 9 x } \
6 & - e ^ { 8 x }
\end{array} \right]$$
A) $- 7 e ^ { 9 x }$
B) $- e ^ { 8 x } - 6 e ^ { 9 x }$
C) $- 5 e ^ { 9 x }$
D) $7 e ^ { 9 x }$

Quizplus · Accepted Answer

The determinant of a 2x2 matrix $\left[ \begin{array} { c c } a & b \ c & d \end{array} \right]$ is calculated as $ad - bc$. For matrix $A$, it is $e^x(-e^{8x}) - (e^{9x})(6) = -e^{9x} - 6e^{9x} = -7e^{9x}$.

Choose the One Alternative That Best Completes the Statement or Answers