91Ó°ÊÓ

Find the area of the triangle shown at the right.

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

14.$\left[\begin{array}{c}4\\ 1\\ −2\end{array}\right]+\left[\begin{array}{c}6\\ −5\\ 8\end{array}\right]$

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

$2r-s=1$

$3r+2s=19$

Triangle $DEF$ with vertices $D\left(1,4\right),\text{E}\left(2,-5\right),\text{and}F\left(-6,-6\right)$ is translated 4 units left and 2 units up.

14. Graph the preimage and the image.

Determine whether each pair of matrices are inverses.14.

$\mathbf{C}\mathbf{=}\left[\begin{array}{cc}1& 5\\ 1& -2\end{array}\right]$

$\mathbf{D}\mathbf{=}\left[\begin{array}{cc}\frac{2}{7}& \frac{5}{7}\\ \frac{1}{7}& \mathbf{-}\frac{1}{7}\end{array}\right]$

State the dimensions of each matrix.

14.$\left[\begin{array}{ccccc}17& −2& 8& −9& 6\\ 5& 11& 20& −1& 4\end{array}\right]$

State the dimensions of each matrix.

$\left[\begin{array}{cc}16& 8\\ 10& 5\\ 0& 0\end{array}\right]$

Find the value of each determinant.

15.$\left|\begin{array}{cc}10& 6\\ 5& 5\end{array}\right|$

Determine whether each pair of matrices are inverses.15.

$\mathbf{J}\mathbf{=}\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 1\\ 1& 1& 2\end{array}\right]$

$\mathbf{K}\mathbf{=}\left[\begin{array}{ccc}\frac{-5}{4}& \frac{1}{4}& \frac{7}{4}\\ \frac{3}{4}& \frac{1}{4}& \mathbf{-}\frac{5}{4}\\ \frac{1}{4}& \mathbf{-}\frac{1}{4}& \frac{1}{4}\end{array}\right]$

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

$3a+5b=33$

$5a+7b=51$