Find the inverse, if it exists, for the matrix.
-$$\left[ \begin{array} { r r }
- 3 & - 2 \
0 & 5
\end{array} \right]$$
A)
$$\left[ \begin{array} { c }
\frac { 1 } { 5 } - \frac { 2 } { 15 } \
0 - \frac { 1 } { 3 }
\end{array} \right]$$
B)
$$\left[ \begin{array} { r r }
- \frac { 1 } { 3 } & \frac { 2 } { 15 } \
0 & \frac { 1 } { 5 }
\end{array} \right]$$
C)
$$\left[ \begin{array} { c c }
0 & \frac { 1 } { 5 } \
- \frac { 1 } { 3 } - \frac { 2 } { 15 }
\end{array} \right]$$

D)
$$\left[ \begin{array} { r r }
- \frac { 1 } { 3 } & - \frac { 2 } { 15 } \
0 & \frac { 1 } { 5 }
\end{array} \right]$$

Question

Find the inverse, if it exists, for the matrix.
-$$\left[ \begin{array} { r r } 
- 3 & - 2 \
0 & 5
\end{array} \right]$$
A)
$$\left[ \begin{array} { c } 
\frac { 1 } { 5 } - \frac { 2 } { 15 } \
0 - \frac { 1 } { 3 }
\end{array} \right]$$
B)
$$\left[ \begin{array} { r r } 
- \frac { 1 } { 3 } & \frac { 2 } { 15 } \
0 & \frac { 1 } { 5 }
\end{array} \right]$$
C)
$$\left[ \begin{array} { c c } 
0 & \frac { 1 } { 5 } \
- \frac { 1 } { 3 } - \frac { 2 } { 15 }
\end{array} \right]$$

D)
$$\left[ \begin{array} { r r } 
- \frac { 1 } { 3 } & - \frac { 2 } { 15 } \
0 & \frac { 1 } { 5 }
\end{array} \right]$$

Quizplus · Accepted Answer

The inverse of a 2x2 matrix $\left[ \begin{array} { c c } a & b \ c & d \end{array} \right]$ is $\frac{1}{ad-bc}\left[ \begin{array} { c c } d & -b \ -c & a \end{array} \right]$. For the given matrix, $a = -3$, $b = -2$, $c = 0$, and $d = 5$, so the determinant $ad-bc = (-3)(5) - (0)(-2) = -15$. The inverse is $\frac{1}{-15}\left[ \begin{array} { c c } 5 & 2 \ 0 & -3 \end{array} \right] = \left[ \begin{array} { r r } - \frac { 1 } { 3 } & - \frac { 2 } { 15 } \ 0 & \frac { 1 } { 5 } \end{array} \right]$.

Find the Inverse, If It Exists, for the Matrix [−3−205]\left[ \begin{array} { r r } - 3 & - 2 \\0 & 5\end{array} \right][−30​−25​]

Find the Inverse, If It Exists, for the Matrix $\left[ \begin{array} { r r } - 3 & - 2 \\0 & 5\end{array} \right]$