# Solving Matrix Equations Worksheets

We are going to explore a technique to help us better understand how to process linear system of equations. We have learned how to process them with the use of the elimination or substitution technique. This gives you another tactic for tackling them through the use of matrices. When you are working at scale, this is a very helpful technique that can save you time. This collective of worksheets and lessons can be used by students and teachers to solve systems using a matrices.

### Aligned Standard: HSA-REI.C.8

- Augmented Matrices Step-by-step Lesson- Matrices do use a considerable amount of space to work with.
- Guided Lesson - If you can really get a good handle on these problems you will be ready to break through to the next level algebra.
- Guided Lesson Explanation -This was a bit look and drawn out to make sure it was properly explained.
- Practice Worksheet - See if you can find the cost breakdown, it will also make it easy to determine good deals.
- Matching Worksheet - Match the scenarios and systems to their final outcome.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

It is very important for students to deeply understand this skill.

- Homework 1 - Use elementary row operations to transform the left part of the augmented matrix into the identity matrix.
- Homework 2 - Smith went shopping with his friend. He puts in two orders at the clothing shop. The first order was for 7 shirts and 5 pants, at a cost of $550. The second order was 1 shirt at a cost of $25. How much does a pair of pants cost?
- Homework 3 - State the solution. Use these three operations to make the part of the matrix to the left of the dashed line look like the identity matrix.

### Practice Worksheets

I start out with a moderate difficulty here.

- Practice 1 - Solve using augmented matrices. You will need to reshape them as an identity matrix first.
- Practice 2 - Start with the augmented matrix from step 1. This gives you some go practice.
- Practice 3 - I like to plug in here. I would suggest you raise the coefficients to 1, when they are not present.

### Math Skill Quizzes

I made the middle quiz a little too easy, I think. I wrote to just give students an easy way to check their work. I write more challenging work for this soon.

- Quiz 1 - Don't lose sight of the end goal here. Let's see how well you understand this topic.
- Quiz 2 - John went to a juice shop with his friend. He placed an order of 6 glasses of mango juice and 18 glasses of pineapple juice at the cost of $630. He placed second order that was 1 glass of mango juice at the cost of $30. How much do the items cost?
- Quiz 3 - Take your time with some of these problems. They may be a little more complicated.

### How Do You Represent Linear Equations Using Matrices?

Linear equations are a type of algebraic equation. Expression with the highest power of variables equals to 1 are called linear equations. Expressions in a linear equation have only one variable. Let's look at a few examples: 10x + 25 + 70, X + 7 = 30, 7 + 4y = 19

A linear equation can also have the same set of variables, the value of x associated with different constants. An equation is also linear when there are multiple variables involved with each of their values already defined prior to solving the equation. For example: 3x + 2y - z = 1 (x = 1, y = -2, z = -1)

A matrix equation is an equation where a variable is a matrix. A matrix is rectangular arrangement of data found in rows and columns, like a spreadsheet. Matrices can be used to compact vast amounts of data in a neat and concise manner. We can also use matrices to solve systems of linear equations. They are not written in a normal or conventional equation form and is usually denoted by a square bracket. When linear equations are found in this form it is called and augmented matrix. Each row represents one equation in the system and the columns represents constants or variables.

### How to Solve Linear Systems Using Augmented Matrices

This is a simple three step process. You first write the system of linear equation as an augmented matrix. You then use elementary row operations to transform the left part of the augmented matrix into the identity matrix. The last thing you need to do is state the solution which will sometimes require you to process a calculation.