Find the inverse of the matrix $\left[ \begin{array} { c c }
3 & 6 \
- 9 & - 15
\end{array} \right]$ .
A) $\frac { 1 } { 7 } \left[ \begin{array} { c c }
3 & 6 \
- 9 & - 15
\end{array} \right]$
B) $\frac { 1 } { 3 } \left[ \begin{array} { c c }
- 5 & - 2 \
3 & 1
\end{array} \right]$
C) $\left[ \begin{array} { c c }
- 3 & - 6 \
15 & 9
\end{array} \right]$
D) $\left[ \begin{array} { c c }
3 & - 9 \
12 & - 21
\end{array} \right]$
E) $\frac { 1 } { 13 } \left[ \begin{array} { l l }
- 3 & - 6 \
- 9 & 15
\end{array} \right]$

Question

Find the inverse of the matrix $\left[ \begin{array} { c c } 
3 & 6 \
- 9 & - 15
\end{array} \right]$ .
A)  $\frac { 1 } { 7 } \left[ \begin{array} { c c } 
3 & 6 \
- 9 & - 15
\end{array} \right]$
B)  $\frac { 1 } { 3 } \left[ \begin{array} { c c } 
- 5 & - 2 \
3 & 1
\end{array} \right]$
C)  $\left[ \begin{array} { c c } 
- 3 & - 6 \
15 & 9
\end{array} \right]$
D)  $\left[ \begin{array} { c c } 
3 & - 9 \
12 & - 21
\end{array} \right]$
E)  $\frac { 1 } { 13 } \left[ \begin{array} { l l } 
- 3 & - 6 \
- 9 & 15
\end{array} \right]$

Quizplus · Accepted Answer

The determinant of the matrix is $3(-15) - 6(-9) = -45 + 54 = 9$. The inverse of a 2x2 matrix $\left[ \begin{array} { c c } a & b \ c & d \end{array} \right]$ is $\frac{1}{ad-bc}\left[ \begin{array} { c c } d & -b \ -c & a \end{array} \right]$. Applying this formula, the inverse is $\frac{1}{9}\left[ \begin{array} { c c } -15 & -6 \ 9 & 3 \end{array} \right] = \frac{1}{3}\left[ \begin{array} { c c } -5 & -2 \ 3 & 1 \end{array} \right]$.

Find the Inverse of the Matrix [36−9−15]\left[ \begin{array} { c c } 3 & 6 \\- 9 & - 15\end{array} \right][3−9​6−15​]

Find the Inverse of the Matrix $\left[ \begin{array} { c c } 3 & 6 \\- 9 & - 15\end{array} \right]$