Use row reduction to find the inverse of the given matrix, if it exists. Check your answers by multiplication.
$\left[ \begin{array} { l l }
3 & 1 \
5 & 2
\end{array} \right]$
A) $\left[ \begin{array} { c c }
2 & - 1 \
- 5 & 3
\end{array} \right]$
B) $\left[ \begin{array} { c c }
- 3 & 1 \
5 & - 2
\end{array} \right]$
C) $\left[ \begin{array} { c c }
2 & 5 \
- 1 & 3
\end{array} \right]$
D) $\left[ \begin{array} { c c }
1 & - 3 \
- 2 & 5
\end{array} \right]$
E) The inverse matrix does not exist.

Question

Use row reduction to find the inverse of the given matrix, if it exists. Check your answers by multiplication.   
$\left[ \begin{array} { l l } 
3 & 1 \
5 & 2
\end{array} \right]$  
A) $\left[ \begin{array} { c c } 
2 & - 1 \
- 5 & 3
\end{array} \right]$
B) $\left[ \begin{array} { c c } 
- 3 & 1 \
5 & - 2
\end{array} \right]$
C)   $\left[ \begin{array} { c c } 
2 & 5 \
- 1 & 3
\end{array} \right]$
D) $\left[ \begin{array} { c c } 
1 & - 3 \
- 2 & 5
\end{array} \right]$
E) The inverse matrix does not exist.

Quizplus · Accepted Answer

The correct answer is A because the inverse of the given matrix is $\left[ \begin{array} { c c } 2 & - 1 \- 5 & 3\end{array} \right]$. This can be verified by multiplying the given matrix by its inverse, which results in the identity matrix:$\left[ \begin{array} { l l } 3 & 1 \5 & 2\end{array} \right] \left[ \begin{array} { c c } 2 & - 1 \- 5 & 3\end{array} \right] = \left[ \begin{array} { c c } 1 & 0 \0 & 1\end{array} \right]$

Use Row Reduction to Find the Inverse of the Given [3152]\left[ \begin{array} { l l } 3 & 1 \\5 & 2\end{array} \right][35​12​]

Use Row Reduction to Find the Inverse of the Given $\left[ \begin{array} { l l } 3 & 1 \\5 & 2\end{array} \right]$