Find the inverse of the matrix $\left[ \begin{array} { c c }
- 2 & 1 \
5 & 4
\end{array} \right]$ (if it exists).
A) $\frac { 1 } { 13 } \left[ \begin{array} { c c }
4 & - 1 \
- 5 & - 2
\end{array} \right]$
B) $- \frac { 1 } { 13 } \left[ \begin{array} { c c }
4 & - 1 \
- 5 & - 2
\end{array} \right]$
C) $- \frac { 1 } { 13 } \left[ \begin{array} { c c }
- 4 & 1 \
5 & 2
\end{array} \right]$
D) $- \frac { 1 } { 13 } \left[ \begin{array} { c c }
- 2 & 1 \
5 & 4
\end{array} \right]$
E)does not exist

Question

Find the inverse of the matrix $\left[ \begin{array} { c c } 
- 2 & 1 \
5 & 4
\end{array} \right]$ (if it exists).
A)  $\frac { 1 } { 13 } \left[ \begin{array} { c c } 
4 & - 1 \
- 5 & - 2
\end{array} \right]$
B)  $- \frac { 1 } { 13 } \left[ \begin{array} { c c } 
4 & - 1 \
- 5 & - 2
\end{array} \right]$
C)  $- \frac { 1 } { 13 } \left[ \begin{array} { c c } 
- 4 & 1 \
5 & 2
\end{array} \right]$
D) $- \frac { 1 } { 13 } \left[ \begin{array} { c c } 
- 2 & 1 \
5 & 4
\end{array} \right]$
E)does not exist

Quizplus · Accepted Answer

The inverse of a 2x2 matrix $\left[ \begin{array} { c c } a & b \ c & d \end{array} \right]$ is given by $\frac{1}{ad-bc} \left[ \begin{array} { c c } d & -b \ -c & a \end{array} \right]$ if $ad-bc \neq 0$. For the given matrix, the determinant is $(-2)(4) - (1)(5) = -8 - 5 = -13$. Thus, the inverse is $-\frac{1}{13} \left[ \begin{array} { c c } 4 & -1 \ -5 & -2 \end{array} \right]$.

Find the Inverse of the Matrix [−2154]\left[ \begin{array} { c c } - 2 & 1 \\5 & 4\end{array} \right][−25​14​]

Find the Inverse of the Matrix $\left[ \begin{array} { c c } - 2 & 1 \\5 & 4\end{array} \right]$