Find the inverse of the matrix.
-$$\left[ \begin{array} { r r }
2 & 5 \
- 5 & - 3
\end{array} \right]$$

A) $\left[ \begin{array} { c c } - \frac { 3 } { 19 } & - \frac { 5 } { 19 } \ \frac { 5 } { 19 } & \frac { 2 } { 19 } \end{array} \right]$

B) $\left[ \begin{array} { c c } - \frac { 3 } { 19 } & \frac { 5 } { 19 } \ - \frac { 5 } { 19 } & \frac { 2 } { 19 } \end{array} \right]$

C) $\left[ \begin{array} { l } \frac { 2 } { 19 } - \frac { 5 } { 19 } \ \frac { 5 } { 19 } - \frac { 3 } { 19 } \end{array} \right]$

D) $\left[ \begin{array} { c c } \frac { 5 } { 19 } & \frac { 2 } { 19 } \ - \frac { 3 } { 19 } & - \frac { 5 } { 19 } \end{array} \right]$

Question

Find the inverse of the matrix.
-$$\left[ \begin{array} { r r } 
2 & 5 \
- 5 & - 3
\end{array} \right]$$

A) $\left[ \begin{array} { c c } - \frac { 3 } { 19 } & - \frac { 5 } { 19 } \ \frac { 5 } { 19 } & \frac { 2 } { 19 } \end{array} \right]$

B) $\left[ \begin{array} { c c } - \frac { 3 } { 19 } & \frac { 5 } { 19 } \ - \frac { 5 } { 19 } & \frac { 2 } { 19 } \end{array} \right]$

C) $\left[ \begin{array} { l } \frac { 2 } { 19 } - \frac { 5 } { 19 } \ \frac { 5 } { 19 } - \frac { 3 } { 19 } \end{array} \right]$

D) $\left[ \begin{array} { c c } \frac { 5 } { 19 } & \frac { 2 } { 19 } \ - \frac { 3 } { 19 } & - \frac { 5 } { 19 } \end{array} \right]$

Quizplus · Accepted Answer

The inverse of a 2x2 matrix $\left[ \begin{array} { r r } a & b \ c & d \end{array} \right]$ is given by $\frac{1}{ad-bc}\left[ \begin{array} { r r } d & -b \ -c & a \end{array} \right]$. For the given matrix, $ad-bc = 2(-3) - (5)(-5) = -6 + 25 = 19$. Thus, the inverse is $\frac{1}{19}\left[ \begin{array} { r r } -3 & -5 \ 5 & 2 \end{array} \right]$, which simplifies to choice A.

Find the Inverse of the Matrix [25−5−3]\left[ \begin{array} { r r } 2 & 5 \\- 5 & - 3\end{array} \right][2−5​5−3​]

Find the Inverse of the Matrix $\left[ \begin{array} { r r } 2 & 5 \\- 5 & - 3\end{array} \right]$