Lesson 7 Transformations with Matrices Solidify Understanding

Ready

Solve each system of equations.

1.

${\begin{matrix} 12 x - 4 y = 20 \\ 5 x + 4 y = 14 \end{matrix}$

2.

${\begin{matrix} 33 x + 24 y = - 12 \\ - 11 x + 2 y = 24 \end{matrix}$

3.

${\begin{matrix} - 5 x + 30 y = 20 \\ - 10 x + 20 y = - 40 \end{matrix}$

4.

${\begin{matrix} 7 x + 6 y = 21 \\ - 3 x + 2 y = 7 \end{matrix}$

Set

5.

Create a matrix with values from these coordinates: $(- 2, 4)$ , $(0, 0)$ , $(5, - 2)$ , $(3, 2)$ . The $x$ -values will be in the top row, and the $y$ -values will be in the bottom row.

$\begin{array}{rc} \begin{array}{cccc} Point & Point & Point & Point \\ 1 & 2 & 3 & 4 \end{array} \\ \begin{array}{rcc} x \\ y \end{array} & [\begin{array}{cccc} \underset{―}{} & \underset{―}{} & \underset{―}{} & \underset{―}{} \\ \underset{―}{} & \underset{―}{} & \underset{―}{} & \underset{―}{} \end{array}] \end{array}$

6.

Multiply the transformation matrix $[\begin{array}{rr} 0 & - 1 \\ 1 & 0 \end{array}]$ times the matrix $[\begin{array}{rrrr} - 2 & 0 & 5 & 3 \\ 4 & 0 & - 2 & 2 \end{array}]$ .

7.

Plot the original parallelogram with coordinates $(- 2, 4)$ , $(0, 0)$ , $(5, - 2)$ , $(3, 2)$ . Then, use the points from the matrix created in problem 6 and plot them on the following coordinate grid. Connect those four points to make a quadrilateral. What transformation occurred between the original parallelogram and the new one?

Go

8.

Function $f (x)$ is defined by the given table.

Write an equation for $f (x)$ .
Fill in the values for $g (x)$ assuming that $g (x) = f (x) + 3$ .
Write an equation for $g (x)$ .
Fill in the values for $h (x)$ assuming that $h (x) = 2 f (x)$ .
Write an equation for $h (x)$ .

$x$	$2$	$4$	$6$	$8$	$10$	$12$	$14$	$16$
$f (x)$	$- 8$	$- 3$	$2$	$7$	$12$	$17$	$22$	$27$
$g (x)$
$h (x)$