Find the inverse of the matrix (if it exists).
$$\left[ \begin{array} { l l }
1 & 2 \
3 & 7
\end{array} \right]$$
A) $\left[ \begin{array} { l l }
7 & 2 \
3 & 1
\end{array} \right]$
B) $\left[ \begin{array} { c c }
7 & - 2 \
- 3 & 1
\end{array} \right]$
C) $\left[ \begin{array} { l l }
- 7 & - 2 \
- 3 & - 1
\end{array} \right]$
D) $\left[ \begin{array} { c c }
- 7 & - 2 \
3 & 1
\end{array} \right]$
E) $\left[ \begin{array} { c c }
- 7 & 2 \
3 & - 1
\end{array} \right]$

Question

Find the inverse of the matrix (if it exists). 
  $$\left[ \begin{array} { l l } 
1 & 2 \
3 & 7
\end{array} \right]$$  
A)  $\left[ \begin{array} { l l } 
7 & 2 \
3 & 1
\end{array} \right]$
B)  $\left[ \begin{array} { c c } 
7 & - 2 \
- 3 & 1
\end{array} \right]$
C)  $\left[ \begin{array} { l l } 
- 7 & - 2 \
- 3 & - 1
\end{array} \right]$
D)  $\left[ \begin{array} { c c } 
- 7 & - 2 \
3 & 1
\end{array} \right]$
E)  $\left[ \begin{array} { c c } 
- 7 & 2 \
3 & - 1
\end{array} \right]$

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, $ad-bc = 1*7 - 2*3 = 7 - 6 = 1$, so the inverse is $\left[ \begin{array} { c c } 7 & -2 \ -3 & 1 \end{array} \right]$.

Find the Inverse of the Matrix (If It Exists) [1237]\left[ \begin{array} { l l } 1 & 2 \\3 & 7\end{array} \right][13​27​]

Find the Inverse of the Matrix (If It Exists) $\left[ \begin{array} { l l } 1 & 2 \\3 & 7\end{array} \right]$