Find the inverse of the matrix $\left[ \begin{array} { c c }
- 3 & - 1 \
- 5 & 0
\end{array} \right]$ (if it exists).
A) $\frac { 1 } { 5 } \left[ \begin{array} { c c }
0 & 1 \
5 & - 3
\end{array} \right]$
B) $- \frac { 1 } { 5 } \left[ \begin{array} { c c }
0 & 1 \
5 & - 3
\end{array} \right]$
C) $- \frac { 1 } { 5 } \left[ \begin{array} { c c }
0 & - 1 \
- 5 & 3
\end{array} \right]$
D) $- \frac { 1 } { 5 } \left[ \begin{array} { c c }
- 3 & - 1 \
- 5 & 0
\end{array} \right]$
E)does not exist

Question

Find the inverse of the matrix $\left[ \begin{array} { c c } 
- 3 & - 1 \
- 5 & 0
\end{array} \right]$ (if it exists).
A) $\frac { 1 } { 5 } \left[ \begin{array} { c c } 
0 & 1 \
5 & - 3
\end{array} \right]$
B) $- \frac { 1 } { 5 } \left[ \begin{array} { c c } 
0 & 1 \
5 & - 3
\end{array} \right]$
C) $- \frac { 1 } { 5 } \left[ \begin{array} { c c } 
0 & - 1 \
- 5 & 3
\end{array} \right]$
D) $- \frac { 1 } { 5 } \left[ \begin{array} { c c } 
- 3 & - 1 \
- 5 & 0
\end{array} \right]$
E)does not exist

Quizplus · Accepted Answer

The determinant of the matrix is $(-3)(0) - (-1)(-5) = -5$. The inverse exists and is given by $-\frac{1}{5} \left[ \begin{array} { c c } 0 & 1 \ 5 & -3 \end{array} \right]$.

Find the Inverse of the Matrix [−3−1−50]\left[ \begin{array} { c c } - 3 & - 1 \\- 5 & 0\end{array} \right][−3−5​−10​]

Find the Inverse of the Matrix $\left[ \begin{array} { c c } - 3 & - 1 \\- 5 & 0\end{array} \right]$