Use the inverse formula $$A ^ { - 1 } = \frac { 1 } { a d - b c } \left[ \begin{array} { c c }
d & - b \
- c & a
\end{array} \right]$$ to find the inverse of the 2×2 matrix (if it exists). $$\left[ \begin{array} { l l }
2 & 3 \
1 & 5
\end{array} \right]$$
A) $$\frac { 1 } { 7 } \left[ \begin{array} { l l }
5 & 3 \
1 & 2
\end{array} \right]$$
B) $$\frac { 1 } { 7 } \left[ \begin{array} { c c }
- 5 & - 3 \
1 & 2
\end{array} \right]$$
C) $$\frac { 1 } { 7 } \left[ \begin{array} { c c }
- 5 & 3 \
1 & - 2
\end{array} \right]$$
D) $$\frac { 1 } { 7 } \left[ \begin{array} { c c }
5 & - 3 \
- 1 & 2
\end{array} \right]$$
E) $$\frac { 1 } { 7 } \left[ \begin{array} { l l }
- 5 & - 3 \
- 1 & - 2
\end{array} \right]$$

Question

Use the inverse formula $$A ^ { - 1 } = \frac { 1 } { a d - b c } \left[ \begin{array} { c c } 
d & - b \
- c & a
\end{array} \right]$$ to find the inverse of the 2×2 matrix (if it exists). ​​ $$\left[ \begin{array} { l l } 
2 & 3 \
1 & 5
\end{array} \right]$$ ​
A)​ $$\frac { 1 } { 7 } \left[ \begin{array} { l l } 
5 & 3 \
1 & 2
\end{array} \right]$$
B)​ $$\frac { 1 } { 7 } \left[ \begin{array} { c c } 
- 5 & - 3 \
1 & 2
\end{array} \right]$$
C)​ $$\frac { 1 } { 7 } \left[ \begin{array} { c c } 
- 5 & 3 \
1 & - 2
\end{array} \right]$$
D)​ $$\frac { 1 } { 7 } \left[ \begin{array} { c c } 
5 & - 3 \
- 1 & 2
\end{array} \right]$$
E)​ $$\frac { 1 } { 7 } \left[ \begin{array} { l l } 
- 5 & - 3 \
- 1 & - 2
\end{array} \right]$$

Quizplus · Accepted Answer

The Answer is D

Use the Inverse Formula A−1=1ad−bc[d−b−ca]A ^ { - 1 } = \frac { 1 } { a d - b c } \left[ \begin{array} { c c } d & - b \\- c & a\end{array} \right]A−1=ad−bc1​[d−c​−ba​]

Use the Inverse Formula $A ^ { - 1 } = \frac { 1 } { a d - b c } \left[ \begin{array} { c c } d & - b \\- c & a\end{array} \right]$