Find the inverse of the invertible matrix.
-$$\left[ \begin{array} { c c }
5 & 5 \
- 5 & 0
\end{array} \right]$$
A) $\left[ \begin{array} { l l } 0 & - \frac { 1 } { 5 } \ \frac { 1 } { 5 } & \frac { 1 } { 5 } \end{array} \right]$
B) $\left[ \begin{array} { c c } \frac { 1 } { 5 } & \frac { 1 } { 5 } \ 0 & - \frac { 1 } { 5 } \end{array} \right]$
C) $\left[ \begin{array} { c c } \frac { 1 } { 5 } & - \frac { 1 } { 5 } \ \frac { 1 } { 5 } & 0 \end{array} \right]$
D) $\left[ \begin{array} { r r } 0 & \frac { 1 } { 5 } \ - \frac { 1 } { 5 } & \frac { 1 } { 5 } \end{array} \right]$

Question

Find the inverse of the invertible matrix.
-$$\left[ \begin{array} { c c } 
5 & 5 \
- 5 & 0
\end{array} \right]$$
A) $\left[ \begin{array} { l l } 0 & - \frac { 1 } { 5 } \ \frac { 1 } { 5 } & \frac { 1 } { 5 } \end{array} \right]$
B) $\left[ \begin{array} { c c } \frac { 1 } { 5 } & \frac { 1 } { 5 } \ 0 & - \frac { 1 } { 5 } \end{array} \right]$
C) $\left[ \begin{array} { c c } \frac { 1 } { 5 } & - \frac { 1 } { 5 } \ \frac { 1 } { 5 } & 0 \end{array} \right]$
D) $\left[ \begin{array} { r r } 0 & \frac { 1 } { 5 } \ - \frac { 1 } { 5 } & \frac { 1 } { 5 } \end{array} \right]$

Quizplus · Accepted Answer

The inverse of a 2x2 matrix $\left[ \begin{array} { c c } a & b \ c & d \end{array} \right]$ is $\frac{1}{ad-bc}\left[ \begin{array} { r r } d & -b \ -c & a \end{array} \right]$. For the given matrix, $a=5$, $b=5$, $c=-5$, and $d=0$, so the determinant $ad-bc = 5*0 - 5*(-5) = 25$. The inverse is $\frac{1}{25}\left[ \begin{array} { r r } 0 & -5 \ 5 & 5 \end{array} \right] = \left[ \begin{array} { l l } 0 & - \frac { 1 } { 5 } \ \frac { 1 } { 5 } & \frac { 1 } { 5 } \end{array} \right]$.

Find the Inverse of the Invertible Matrix [55−50]\left[ \begin{array} { c c } 5 & 5 \\- 5 & 0\end{array} \right][5−5​50​]

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