Find the inverse of the matrix $\left[ \begin{array} { c c }
2 & 4 \
- 6 & - 10
\end{array} \right]$ .
A) $\frac { 1 } { 13 } \left[ \begin{array} { l l }
- 2 & - 4 \
- 6 & 10
\end{array} \right]$
B) $\left[ \begin{array} { c c }
- 2 & - 4 \
10 & 6
\end{array} \right]$
C) $\left[ \begin{array} { c c }
2 & - 6 \
8 & - 14
\end{array} \right]$
D) $\frac { 1 } { 7 } \left[ \begin{array} { c c }
2 & 4 \
- 6 & - 10
\end{array} \right]$
E) $\frac { 1 } { 2 } \left[ \begin{array} { c c }
- 5 & - 2 \
3 & 1
\end{array} \right]$

Question

Find the inverse of the matrix $\left[ \begin{array} { c c } 
2 & 4 \
- 6 & - 10
\end{array} \right]$ .
A)  $\frac { 1 } { 13 } \left[ \begin{array} { l l } 
- 2 & - 4 \
- 6 & 10
\end{array} \right]$
B)  $\left[ \begin{array} { c c } 
- 2 & - 4 \
10 & 6
\end{array} \right]$
C)  $\left[ \begin{array} { c c } 
2 & - 6 \
8 & - 14
\end{array} \right]$
D)  $\frac { 1 } { 7 } \left[ \begin{array} { c c } 
2 & 4 \
- 6 & - 10
\end{array} \right]$
E)  $\frac { 1 } { 2 } \left[ \begin{array} { c c } 
- 5 & - 2 \
3 & 1
\end{array} \right]$

Quizplus · Accepted Answer

The determinant of the matrix is 2(-10) - 4(-6) = -20 + 24 = 4. The inverse is $\frac{1}{4}$ times the adjugate matrix, which is $\left[ \begin{array} { c c } -10 & -4 \ 6 & 2 \end{array} \right]$. Simplifying gives $\frac{1}{2} \left[ \begin{array} { c c } -5 & -2 \ 3 & 1 \end{array} \right]$.

Find the Inverse of the Matrix [24−6−10]\left[ \begin{array} { c c } 2 & 4 \\- 6 & - 10\end{array} \right][2−6​4−10​]

Find the Inverse of the Matrix $\left[ \begin{array} { c c } 2 & 4 \\- 6 & - 10\end{array} \right]$