Find the inverse of the matrix.
-$$\left[ \begin{array} { r r }
4 & 0 \
- 1 & - 1
\end{array} \right]$$

A) $\left[ \begin{array} { r r } \frac { 1 } { 4 } & 0 \ - \frac { 1 } { 4 } & - 1 \end{array} \right]$

B) $\left[ \begin{array} { c c } - 1 & 0 \ - \frac { 1 } { 4 } & \frac { 1 } { 4 } \end{array} \right]$

C) $\left[ \begin{array} { r r } \frac { 1 } { 4 } & 0 \ \frac { 1 } { 4 } & - 1 \end{array} \right]$

D) No inverse

Question

Find the inverse of the matrix.
-$$\left[ \begin{array} { r r } 
4 & 0 \
- 1 & - 1
\end{array} \right]$$

A) $\left[ \begin{array} { r r } \frac { 1 } { 4 } & 0 \ - \frac { 1 } { 4 } & - 1 \end{array} \right]$

B) $\left[ \begin{array} { c c } - 1 & 0 \ - \frac { 1 } { 4 } & \frac { 1 } { 4 } \end{array} \right]$

C) $\left[ \begin{array} { r r } \frac { 1 } { 4 } & 0 \ \frac { 1 } { 4 } & - 1 \end{array} \right]$

D) No inverse

Quizplus · Accepted Answer

The inverse of a 2x2 matrix $\left[ \begin{array} { r r } a & b \ c & d \end{array} \right]$ is $\frac{1}{ad-bc}\left[ \begin{array} { r r } d & -b \ -c & a \end{array} \right]$. For the given matrix, $ad-bc = 4(-1)-0(-1) = -4$, so its inverse is $\frac{1}{-4}\left[ \begin{array} { r r } -1 & 0 \ 1 & 4 \end{array} \right] = \left[ \begin{array} { r r } \frac { 1 } { 4 } & 0 \ - \frac { 1 } { 4 } & - 1 \end{array} \right]$.

Find the Inverse of the Matrix [40−1−1]\left[ \begin{array} { r r } 4 & 0 \\- 1 & - 1\end{array} \right][4−1​0−1​]

Find the Inverse of the Matrix $\left[ \begin{array} { r r } 4 & 0 \\- 1 & - 1\end{array} \right]$