Find the inverse of the matrix if it exists. $$\left[ \begin{array} { l l }
5 & 2 \
4 & 9
\end{array} \right]$$
A) $$9 \left[ \begin{array} { l l }
5 & 4 \
2 & 1
\end{array} \right]$$
B) $$\frac { 1 } { 5 } \left[ \begin{array} { c c }
9 & 4 \
- 2 & 37
\end{array} \right]$$
C) $$\frac { 1 } { 37 } \left[ \begin{array} { c c }
9 & - 2 \
- 4 & 5
\end{array} \right]$$
D) $$\frac { 1 } { 37 } \left[ \begin{array} { c c }
63 & - 14 \
- 28 & 35
\end{array} \right]$$
E) Does not exist

Question

Find the inverse of the matrix if it exists. $$\left[ \begin{array} { l l } 
5 & 2 \
4 & 9
\end{array} \right]$$
A) $$9 \left[ \begin{array} { l l } 
5 & 4 \
2 & 1
\end{array} \right]$$
B) $$\frac { 1 } { 5 } \left[ \begin{array} { c c } 
9 & 4 \
- 2 & 37
\end{array} \right]$$
C) $$\frac { 1 } { 37 } \left[ \begin{array} { c c } 
9 & - 2 \
- 4 & 5
\end{array} \right]$$
D) $$\frac { 1 } { 37 } \left[ \begin{array} { c c } 
63 & - 14 \
- 28 & 35
\end{array} \right]$$
E) Does not exist

Quizplus · Accepted Answer

The inverse of a 2x2 matrix $\left[ \begin{array} { l l } a & b \ c & d \end{array} \right]$ 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, $ad-bc = 5*9 - 2*4 = 37$, so the inverse exists and is $\frac{1}{37} \left[ \begin{array} { c c } 9 & -2 \ -4 & 5 \end{array} \right]$.

Find the Inverse of the Matrix If It Exists [5249]\left[ \begin{array} { l l } 5 & 2 \\4 & 9\end{array} \right][54​29​]

Find the Inverse of the Matrix If It Exists $\left[ \begin{array} { l l } 5 & 2 \\4 & 9\end{array} \right]$