What is element $a _ { 11 }$ of the inverse of the following matrix?
$$\left[ \begin{array} { c c }
16 & 1 \
1 & 8
\end{array} \right]$$
A) $\frac { 8 } { 257 }$
B) $\frac { 8 } { 127 }$
C) $- \frac { 16 } { 127 }$
D) $- \frac { 8 } { 127 }$
E) $\frac { 16 } { 127 }$

Question

What is element $a _ { 11 }$ of the inverse of the following matrix?
$$\left[ \begin{array} { c c } 
16 & 1 \
1 & 8
\end{array} \right]$$
A) $\frac { 8 } { 257 }$
B) $\frac { 8 } { 127 }$
C) $- \frac { 16 } { 127 }$
D) $- \frac { 8 } { 127 }$
E) $\frac { 16 } { 127 }$

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 $d/\text{det}(A)$, where $\text{det}(A) = ad - bc$. For the given matrix, $a = 16$, $b = 1$, $c = 1$, $d = 8$, so $\text{det}(A) = 16*8 - 1*1 = 127$. Therefore, $a_{11} = 8/127$.

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