## Matrices

Practice Quiz for Chapter 2.1-2.4 / Solutions

After we have covered sections 2.1-2.4 in class, then do the practice quiz to self
assess your understanding of the Matrix topics before the exam.

The practice quiz is not included in your grade. You do not turn it in. Use it for
studying for exam.

Quiz document and quiz key document (pdf files) should open in a new window or tab.

### Homework and Resources

#### Section 2.1

- Do problems 1 thru 5, 7, 10, 11, 14-19, 21

##### Video Example

Video example for matrix multiplication, by PatrickJMT https://www.youtube.com/watch?v=sYlOjyPyX3g

#### Section 2.2

- Solve using Gauss Jordan Method: 4x + 12y = 52 , 2x + y = −9
- Do problems 1-4 in textbook

##### Video Examples

Video examples using Row Operations with the Gauss Jordan Method of Elimination to get Reduced Row Echelon form.

- Gauss-Jordan Row Reduced Echelon Method

This video shows a system of 2 equations and 2 variables. The instructor in the video writes a lot more of the arithmetic work on her paper, but she is doing the same process. The arithmetic is a little harder (some fractions) than the examples I did in class. - Solving Linear Equations by using the Gauss-Jordan Elimination Method

This video also shows a system of 2 equations and 2 variables. - Row Reduced Echelon Form

This video shows a system of 3 equations and 3 variables.

To check your answers in Section 2.2 you can:

- substitute your answers into the equations and check if your answers satisfy all the
equations

OR - go to Wolfram Alpha and input your equations to get the answer.

Wolfram Alpha will give you answers for free,but not worked out solutions

OR - put the augmented matrix into your calculator using 2nd MATRIX EDIT

Use 2nd MATRIX MATH B:rref with your matrix name from the MATRIX menu to get the answer. You will be required to show work written out using the requested method(s) on quizzes or exams, but you can use this on your calculator to check your solution.

Your calculator has built in row operation functions for Matrices

I think its harder to do using the calculator than by hand, since I usually make questions with fairly easy arithmetic for exams and quizzes.

I find it hard to remember how to use the row operation commands correctly as you need to put the input in exactly correctly in the right order or the calculator will do the wrong thing.

If you want instructions, watch this video from the Learning Assistance Center at Howard Community College. I will not teach this calculator method because I think its easier and faster to do by hand. If you want to learn the calculator commands from this video, you can use this method on the calculator for homework, tests and quizzes. But I can not help you with this on the calculator

#### Section 2.3

- Do problems 1, 3, 5, 8, 9
- Also do review problems 8a, 8b from section 2.7

#### Section 2.4

- Do problems 1, 3, 4, 5, 7, 8, 9, 10
- Please Note:
- Problem 7 uses A
^{-1}from problem 3 - Problem 8 uses A
^{-1}from problem 4 - Problem 9 uses A
^{-1}from problem 5 - Problem 10 uses A
^{-1}from problem 6, which was not assigned, so just use the calculator to find A^{-1}using the x^{-1}inverse key.

- Problem 7 uses A