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 inverse of a 2x2 matrix $\left[ \begin{array} { c c } a & b \ c & d \end{array} \right]$ is given by $\frac{1}{ad-bc} \left[ \begin{array} { c c } d & -b \ -c & a \end{array} \right]$, provided that $ad-bc \neq 0$. For the given matrix, $a=3$, $b=6$, $c=-9$, and $d=-15$. The determinant is $ad-bc = (3)(-15) - (6)(-9) = -45 + 54 = 9$. Thus, 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 $\left[ \begin{array} { c c } 3 & 6 \\- 9 & - 15\end{array} \right]$