91Ó°ÊÓ

Find the inverse of each matrix, if it exists.20.

$\left[\begin{array}{cc}5& 0\\ 0& 1\end{array}\right]$

For exercises 18-20, use the following information

The vertices of $\mathrm{Δ}XYZ$ are $X\left(1,-1\right),Y\left(2,-4\right),\text{and}Z\left(7,-1\right)$. The triangle is reflected over the line $y=x$

20. Graph $\mathrm{Δ}XYZ$ and $\mathrm{Δ}X\text{'}Y\text{'}Z\text{'}$

Find the value of each determinant.

20.$\left|\begin{array}{cc}−6& −2\\ 8& 5\end{array}\right|$

Solve each equation.

$\left[\begin{array}{c}x+3y\\ 3x+y\end{array}\right]\mathbf{=}\left[\begin{array}{c}-13\\ 1\end{array}\right]$

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

$\left[\begin{array}{cc}1.35& 5.80\\ 1.24& 14.32\\ 6.10& 35.26\end{array}\right]+\left[\begin{array}{cc}0.45& 3.28\\ 1.94& 16.72\\ 4.31& 21.30\end{array}\right]$

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

$3x-2y=4$

$\frac{1}{2}x-\frac{2}{3}y=1$

Find each product, if possible.

$\left[\begin{array}{cc}3& −2\\ 5& 1\end{array}\right]â‹\dots \left[\begin{array}{cc}4& 1\\ 2& 7\end{array}\right]$

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.

21. Write the coordinates of the parallelogram in a vertex matrix.

Find the value of each determinant.

$\left|\begin{array}{cc}−9& 0\\ −12& −7\end{array}\right|$

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

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