Find the inverse of the matrix.
-$$\left[ \begin{array} { r r }
1 & 1 \
3 & - 1
\end{array} \right]$$
A) $\left[ \begin{array} { l l } \frac { 3 } { 4 } & - \frac { 1 } { 4 } \ \frac { 1 } { 4 } & \frac { 1 } { 4 } \end{array} \right]$

B) $\left[ \begin{array} { r } - \frac { 1 } { 4 } \frac { 1 } { 4 } \ \frac { 3 } { 4 } \frac { 1 } { 4 } \end{array} \right]$

C) $\left[ \begin{array} { c c } \frac { 1 } { 4 } & \frac { 1 } { 4 } \ \frac { 3 } { 4 } & - \frac { 1 } { 4 } \end{array} \right]$

D) $\left[ \begin{array} { r } \frac { 1 } { 4 } - \frac { 1 } { 4 } \ - \frac { 3 } { 4 } - \frac { 1 } { 4 } \end{array} \right]$

Question

Find the inverse of the matrix.
-$$\left[ \begin{array} { r r } 
1 & 1 \
3 & - 1
\end{array} \right]$$
A) $\left[ \begin{array} { l l } \frac { 3 } { 4 } & - \frac { 1 } { 4 } \ \frac { 1 } { 4 } & \frac { 1 } { 4 } \end{array} \right]$

B) $\left[ \begin{array} { r } - \frac { 1 } { 4 } \frac { 1 } { 4 } \ \frac { 3 } { 4 } \frac { 1 } { 4 } \end{array} \right]$

C) $\left[ \begin{array} { c c } \frac { 1 } { 4 } & \frac { 1 } { 4 } \ \frac { 3 } { 4 } & - \frac { 1 } { 4 } \end{array} \right]$

D) $\left[ \begin{array} { r } \frac { 1 } { 4 } - \frac { 1 } { 4 } \ - \frac { 3 } { 4 } - \frac { 1 } { 4 } \end{array} \right]$

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, the determinant is $1(-1) - 1(3) = -4$. The inverse is $\frac{1}{-4} \left[ \begin{array} { r r } -1 & -1 \ -3 & 1 \end{array} \right]$, which simplifies to $\left[ \begin{array} { c c } \frac { 1 } { 4 } & \frac { 1 } { 4 } \ \frac { 3 } { 4 } & - \frac { 1 } { 4 } \end{array} \right]$.

Find the Inverse of the Matrix [113−1]\left[ \begin{array} { r r } 1 & 1 \\3 & - 1\end{array} \right][13​1−1​]

Find the Inverse of the Matrix $\left[ \begin{array} { r r } 1 & 1 \\3 & - 1\end{array} \right]$