Use a graphing calculator to find the inverse of the matrix. Give five decimal places, if necessary.
-$$A = \left[ \begin{array} { c c }
\frac { 4 } { 3 } & 52 \
\sqrt { 21 } & 8.754
\end{array} \right]$$

A)
$$\left[ \begin{array} { c c }
0.75 & 0.01923 \
0.21822 & 0.11423
\end{array} \right]$$
B)
$$\left[ \begin{array} { r r }
- 0.03863 & 0.22946 \
0.02022 & - 0.00588
\end{array} \right]$$
C)
$$\left[ \begin{array} { r r }
- 0.70513 & 0.41667 \
0.36859 & - 0.10417
\end{array} \right]$$
D)
$$\left[ \begin{array} { l l }
1 & 0 \
0 & 1
\end{array} \right]$$

Question

Use a graphing calculator to find the inverse of the matrix. Give five decimal places, if necessary.
-$$A = \left[ \begin{array} { c c } 
\frac { 4 } { 3 } & 52 \
\sqrt { 21 } & 8.754
\end{array} \right]$$

A)
$$\left[ \begin{array} { c c } 
0.75 & 0.01923 \
0.21822 & 0.11423
\end{array} \right]$$
B)
$$\left[ \begin{array} { r r } 
- 0.03863 & 0.22946 \
0.02022 & - 0.00588
\end{array} \right]$$
C)
$$\left[ \begin{array} { r r } 
- 0.70513 & 0.41667 \
0.36859 & - 0.10417
\end{array} \right]$$
D)
$$\left[ \begin{array} { l l } 
1 & 0 \
0 & 1
\end{array} \right]$$

Quizplus · Accepted Answer

The inverse of a matrix $A$ is found using the formula $A^{-1} = \frac{1}{\text{det}(A)} \text{adj}(A)$, where $\text{det}(A)$ is the determinant of $A$ and $\text{adj}(A)$ is the adjugate of $A$. The determinant of $A$ can be calculated as $\text{det}(A) = a_{11}a_{22} - a_{12}a_{21}$, and the adjugate involves swapping the diagonal elements, changing the signs of the off-diagonal elements, and then transposing the matrix if necessary. The given matrix has unique real numbers and does not resemble the identity matrix, making options A, C, and D less likely without calculation. Using a graphing calculator to perform the exact calculation confirms option B as the correct inverse with precise decimal values.

Use a Graphing Calculator to Find the Inverse of the Matrix