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 matrix (if it exists).
$\left[ \begin{array} { c c }
- 7 & - 9 \
7 & 9
\end{array} \right]$
A) $\left[ \begin{array} { c c }
- 9 & - 9 \
7 & 7
\end{array} \right]$
B) $\left[ \begin{array} { r r }
- 9 & - 9 \
- 7 & - 7
\end{array} \right]$
C) $\left[ \begin{array} { c c }
- 9 & 9 \
7 & - 7
\end{array} \right]$
D) $\left[ \begin{array} { c c }
9 & - 9 \
7 & 7
\end{array} \right]$
E) Does not exist

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 matrix (if it exists).  
  $\left[ \begin{array} { c c } 
- 7 & - 9 \
7 & 9
\end{array} \right]$  
A)  $\left[ \begin{array} { c c } 
- 9 & - 9 \
7 & 7
\end{array} \right]$
B)  $\left[ \begin{array} { r r } 
- 9 & - 9 \
- 7 & - 7
\end{array} \right]$
C)  $\left[ \begin{array} { c c } 
- 9 & 9 \
7 & - 7
\end{array} \right]$
D) $\left[ \begin{array} { c c } 
9 & - 9 \
7 & 7
\end{array} \right]$
E) Does not exist

Quizplus · Accepted Answer

The determinant of the matrix is $ad - bc = (-7)(9) - (-9)(7) = -63 + 63 = 0$. Since the determinant is 0, the inverse of the matrix does not exist.

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