## Linear Equations as a Matrix Equation

#### Aligned To Common Core Standard:

**High School** - HSA-REI.C.8

What is, are the Differences between Linear Equations and Matrix Equations? 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. 10x + 25 + 70 = 4x An equation is also linear when there are multiple variables involved with each of their values already defined prior to solving the equation. For examples: 3x + 2y – z = 1 (x = 1, y = -2, z = -1) Now let's learn what a matrix equation is. A matrix equation is an equation where a variable is a matrix. It can also be defined as an equation where an entire matrix is available. It is not written in a normal or conventional equation form and is usually denoted by a square bracket. This collective of worksheets and lessons can be used by students and teachers to solve systems using a matrices.

### Printable Worksheets And Lessons

- 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.

#### 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.
- Practice 2 - Start with the augmented matrix from step 1.
- Practice 3 - I like to plug in here.

#### 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.
- 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 - Solve using an augmented matrices.