Find the inverse of the matrix.
-$\left[ \begin{array} { r r } 1 & - 2 \ 6 & 2 \end{array} \right]$
A) $\left[ \begin{array} { c c } \frac { 1 } { 7 } & \frac { 1 } { 7 } \ - \frac { 3 } { 7 } & \frac { 1 } { 14 } \end{array} \right]$
B) $\left[ \begin{array} { c c } - \frac { 3 } { 7 } & \frac { 1 } { 14 } \ \frac { 1 } { 7 } & \frac { 1 } { 7 } \end{array} \right]$
C) $\left[ \begin{array} { c c } \frac { 1 } { 7 } & - \frac { 1 } { 7 } \ \frac { 3 } { 7 } & \frac { 1 } { 14 } \end{array} \right]$
D) $\left[ \begin{array} { c c } \frac { 1 } { 14 } & \frac { 1 } { 7 } \ - \frac { 3 } { 7 } & \frac { 1 } { 7 } \end{array} \right]$

Question

Quizplus · Accepted Answer

The inverse of a 2x2 matrix $\left[ \begin{array} { c c } a & b \ c & d \end{array} \right]$ is $\frac{1}{ad-bc}\left[ \begin{array} { c c } d & -b \ -c & a \end{array} \right]$. For the given matrix, $ad-bc = (1)(2) - (-2)(6) = 2 + 12 = 14$, so the inverse is $\frac{1}{14}\left[ \begin{array} { c c } 2 & 2 \ -6 & 1 \end{array} \right] = \left[ \begin{array} { c c } \frac { 1 } { 7 } & \frac { 1 } { 7 } \ - \frac { 3 } { 7 } & \frac { 1 } { 14 } \end{array} \right]$.

Find the Inverse of the Matrix [1−262]\left[ \begin{array} { r r } 1 & - 2 \\ 6 & 2 \end{array} \right][16​−22​]

Find the Inverse of the Matrix $\left[ \begin{array} { r r } 1 & - 2 \\ 6 & 2 \end{array} \right]$