Find the inverse of the matrix. $$\left[ \begin{array} { c c }
1 & 4 \
- 4 & - 1
\end{array} \right]$$
A) $\left[ \begin{array} { c c } \frac { 1 } { 15 } & - \frac { 4 } { 15 } \ \frac { 4 } { 15 } & \frac { 1 } { 15 } \end{array} \right]$

B)
$\left[ \begin{array} { c c } - \frac { 1 } { 15 } & - \frac { 4 } { 15 } \ - \frac { 4 } { 15 } & \frac { 1 } { 15 } \end{array} \right]$

C)
$\left[\begin{array}{cc}
-\frac{1}{15} & \frac{4}{15} \
\frac{4}{15} & \frac{1}{15}
\end{array}\right]$

D) $\left[ \begin{array} { c c } - \frac { 1 } { 15 } & - \frac { 4 } { 15 } \ \frac { 4 } { 15 } & \frac { 1 } { 15 } \end{array} \right]$

E) $\left[ \begin{array} { c c } - \frac { 1 } { 15 } & - \frac { 4 } { 15 } \ \frac { 4 } { 15 } & - \frac { 1 } { 15 } \end{array} \right]$

Question

Find the inverse of the matrix. $$\left[ \begin{array} { c c } 
1 & 4 \
- 4 & - 1
\end{array} \right]$$
A) $\left[ \begin{array} { c c } \frac { 1 } { 15 } & - \frac { 4 } { 15 } \ \frac { 4 } { 15 } & \frac { 1 } { 15 } \end{array} \right]$

B)
$\left[ \begin{array} { c c } - \frac { 1 } { 15 } & - \frac { 4 } { 15 } \ - \frac { 4 } { 15 } & \frac { 1 } { 15 } \end{array} \right]$

C)
$\left[\begin{array}{cc}
-\frac{1}{15} & \frac{4}{15} \
\frac{4}{15} & \frac{1}{15}
\end{array}\right]$

D) $\left[ \begin{array} { c c } - \frac { 1 } { 15 } & - \frac { 4 } { 15 } \ \frac { 4 } { 15 } & \frac { 1 } { 15 } \end{array} \right]$

E) $\left[ \begin{array} { c c } - \frac { 1 } { 15 } & - \frac { 4 } { 15 } \ \frac { 4 } { 15 } & - \frac { 1 } { 15 } \end{array} \right]$

Quizplus · Accepted Answer

The inverse of a 2x2 matrix $\left[ \begin{array} { c c } a & b \ c & d \end{array} \right]$ is $\frac{1}{ad-bc}\left[ \begin{array} { c c } d & -b \ -c & a \end{array} \right]$. For the given matrix, $ad-bc = (1)(-1) - (4)(-4) = -1 + 16 = 15$, so the inverse is $\frac{1}{15}\left[ \begin{array} { c c } -1 & -4 \ 4 & 1 \end{array} \right]$, which matches option D.

Find the Inverse of the Matrix [14−4−1]\left[ \begin{array} { c c } 1 & 4 \\- 4 & - 1\end{array} \right][1−4​4−1​]

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