91Ó°ÊÓ

Find the inverse of each matrix, if it exists.21.

$\left[\begin{array}{cc}6& 3\\ 8& 4\end{array}\right]$

Solve each equation.

Perform the indicated matrix operation. If the matrix doesn’t exist, write impossible.

21.$8\left[\begin{array}{cc}0.25& 0.5\\ 0.75& 1.5\end{array}\right]−2\left[\begin{array}{cc}0.25& 0.5\\ 0.75& 1.5\end{array}\right]$

Find each product, if possible.

$\left[\begin{array}{ccc}4& −1& 6\\ 1& 5& −8\end{array}\right]â‹\dots \left[\begin{array}{cc}1& 3\\ 9& −6\end{array}\right]$

For exercises 21-23, use the following information

Parallelogram $DEFG$ with $D\left(2,4\right),E\left(5,4\right),F\left(4,1\right),\text{and}G\left(1,1\right)$ is rotated $270°$ counter clockwise about the origin.

22. Find the coordinates of parallelogram $D\text{'}E\text{'}F\text{'}G\text{'}$

Find the inverse of each matrix, if it exists. 22.

$\left[\begin{array}{cc}1& 2\\ 2& 1\end{array}\right]$

Perform the indicated matrix operation. If the matrix doesn’t exist, write impossible.

22.$\frac{1}{2}\left[\begin{array}{cc}4& 6\\ 3& 0\end{array}\right]−\frac{2}{3}\left[\begin{array}{cc}9& 27\\ 0& 3\end{array}\right]$

Find the value of each determinant.

$\left|\begin{array}{cc}6& 14\\ −3& −8\end{array}\right|$

Solve each equation.

$\left[\begin{array}{c}2x\\ 2x+3y\end{array}\right]\mathbf{=}\left[\begin{array}{c}y\\ 12\end{array}\right]$

Use Cramer’s Rule to solve each system of equations.

$\frac{1}{3}r+\frac{2}{5}s=5$

$\frac{2}{3}r-\frac{1}{2}s=-3$