# Inverse of a Matrix Worksheets

Previously we learned about a nice method to hold large amounts of data in the form of a matrix. We then learned how to perform operations across them. An inverse matrix is basically the reciprocal of a set matrices. We will learn how to determine the inverse values of set of matrices. We use this technique to find solutions to linear equations at scale. This form of math is used heavily in Internet security especially encryption. You will also find this frequently used in all different forms of electrical engineering.

### Aligned Standard: HSA-REI.C.9

- Inverse Matrices Step-by-step Lesson- We show you how to compose your first inverse matrix.
- Guided Lesson - See how all of these fit into the standards solving format.
- Guided Lesson Explanation -We go through the basic three steps to solving all of these.
- Practice Worksheet - Practice away with this set and see what you can do to finish it all up.
- Matching Worksheet - Match the inverse to each matrix.

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

### Homework Sheets

I don't ever remember seeing Matrices at the non-honors High School Level until the current set of standards prevailed.

- Homework 1 - Find the inverse of the following matrix.
- Homework 2 - Step 1: Find the pivot in the 1st column in the 1st row Step 2: Eliminate the 1st column
- Homework 3 - Step 3: Make the pivot in the 2nd column by dividing the 2nd row by 3 Step 4: Find the pivot in the 3rd column in the 3rd row

### Practice Worksheets

Sorry for the super long explanations here. I just wanted to make sure to be thorough.

- Practice 1 - Step 3: Make the pivot in the 2nd column by dividing the 3rd row by -6 and swap the 3rd and the 2nd rows Step 4: Eliminate the 2nd column
- Practice 2 - What is the Role of Finding the Inverse of a Matrix?
- Practice 3 - A little binary problem for you.

### Math Skill Quizzes

I continue to pay attention to detail in these as well.

- Quiz 1 - Six problems for you to tussle with. We exclusively focus on the use of 3 x 3 matrices.
- Quiz 2 - Don't lose sight around the negative values. Make sure to accomodate them.
- Quiz 3 - Circle up on yourself. A good way to gauge your level of understanding.

### What is the Inverse of a Matrix?

They say there is always another side to the story, or there are always two sides to get a complete picture. One concept in mathematics that involves having an inverse in it is the concept of Matrix. Matrices are one of the most powerful tools in mathematics. They are the basic part of mathematics and an important concept used in higher studies and real-life problems. They are used to compile large amounts of data into rows and columns. Matrices were discovered to obtain a simple and easy solution for solving the linear equations. But before you go on to finding what the inverse of the matrix is, have a grasp on the basic concept of matrix first.

A matrix is a collection and display of numbers. It is an ordered rectangular arrangement of real or complex numbers. They are often referred to as an array of numbers. They are a great shorthand method for keeping track of large amounts of data. This is used by scientists and engineers to track change within the systems that they are observing or attempting to manipulate.

Inverse means to undo or do the opposite of what has been proposed. In math we have learned that this is the concept of forming a reciprocal where the numerator and denominator switch positions. When we apply this concept to matrices, the inverse of a matrix is the matrix when multiplied by itself, results in the identity. Suppose A is a matrix which, when multiplied by the same A matrix, results in the identity of that particular matrix. The notation for this inverse matrix is A^{-1}. So, if you see that notation placed next to a value, they are asking you to determine the inverse of the value. Here, the important thing to remember is that not all matrices have an inverse. Non-square matrices do not have inverses.