Lesson 5E Solving Systems with Matrices, Revisited Solidify Understanding

Ready

1.

The following three points form the vertices of a triangle: , , .

a blank 17 by 17 grid
  1. Plot these three points on the coordinate grid and then connect them.

  2. Reflect the original triangle over the -axis and record the coordinates of the vertices.

  3. Reflect the original triangle over the -axis and record the coordinates of the vertices.

  4. Rotate the original triangle counterclockwise about the origin and record the coordinates of the vertices.

  5. Rotate the original triangle about the origin and record the coordinates of the vertices.

Set

2.

Two of the following systems have unique solutions (that is, the lines intersect at a single point).

Use the determinant of a matrix to decide which systems have unique solutions, and which one does not.

a.

b.

c.

3.

For each of the systems in problem 2 that have a unique solution, find the solution to the system by solving a matrix equation using an inverse matrix.

a.

b.

c.

Go

Perform the indicated operation. If the operation cannot be performed, state why.

4.

5.

6.

7.

Perform the row operations indicated.

8.

9.

For problems 10 and 11, provide an example using matrices to either illustrate or refute each of the properties below.

10.

Associative Property of Multiplication

11.

Commutative Property of Multiplication