What is element $a _ { 11 }$ of the inverse of the following matrix?
$$\left[ \begin{array} { c c }
8 & 1 \
1 & 16
\end{array} \right]$$
A) $- \frac { 8 } { 127 }$
B) $\frac { 16 } { 127 }$
C) $- \frac { 16 } { 127 }$
D) $\quad \frac { 8 } { 127 }$
E) $\frac { 16 } { 65 }$

Question

What is element $a _ { 11 }$ of the inverse of the following matrix?
$$\left[ \begin{array} { c c } 
8 & 1 \
1 & 16
\end{array} \right]$$
A) $- \frac { 8 } { 127 }$
B) $\frac { 16 } { 127 }$
C) $- \frac { 16 } { 127 }$
D) $\quad \frac { 8 } { 127 }$
E) $\frac { 16 } { 65 }$

Quizplus · Accepted Answer

The element $a_{11}$ of the inverse of a 2x2 matrix $\left[ \begin{array} { c c } a & b \ c & d \end{array} \right]$ is given by $d/D$, where $D = ad - bc$ is the determinant of the matrix. For the given matrix, $a = 8$, $b = 1$, $c = 1$, and $d = 16$, so $D = 8*16 - 1*1 = 128 - 1 = 127$. Therefore, $a_{11} = d/D = 16/127$.

What Is Element a11a _ { 11 }a11​ Of the Inverse of the Following Matrix

What Is Element $a _ { 11 }$ Of the Inverse of the Following Matrix