## Finding the Inverse of a Matrix

#### Aligned To Common Core Standard:

**High School** - HSA-REI.C.9

What is the Inverse of a Matrix? They say there is always another side to the story, or there are always two sides to a 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. 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. On the other hand, what is an inverse of a matrix? 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. Here, the important thing to remember is that not all matrices have an inverse. Non-square matrices do not have inverses.

### Printable Worksheets And Lessons

- 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.

#### 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.