# Determinants and Inverses of Matrices Worksheets

As computer science continues to expand at such a rapid pace, we see that this form of math has many more applications than we first may have thought. It all started with the rise of the Internet. We needed a safe way to make certain that only two of billions of computers were communicating with one another safely. We learned that matrices could be used to encrypt and decrypt information. We now are seeing the rise of the age of artificial intelligence and guess what, this form of math is used now more than ever in that world. In this topic we will look at common operational techniques that are used evaluate data that is suspended within a data matrix. Students will learn how find and use determinants and inverses with matrices.

### Aligned Standard: HSN-VM.C.12

- Determinants Step-by-step Lesson- We work specifically on the more challenging of the two skills of this standard.
- Guided Lesson - Both skills are covered in here like magic! Only real!
- Guided Lesson Explanation - We show you how to find one over a matrix. It's a tough skill for most to get the hang of.
- Practice Worksheet - More determinants and inverses for you to solve.
- Matching Worksheet - A nice package for review or a quick refresher for kids.

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

### Homework Sheets

Sheet 1 = Determinants, Sheet 2 and 3 = The Inverse of 2 x 2 Matrices.

- Homework 1 - Code breakers have used inverse matrices for years to help them decrypt messages.
- Homework 2 - We can express the inverse of a 2 x 2 matrix several ways, we show you one way.
- Homework 3 - An inverse matrix yields the identity matrix when multiplied by the original matrix.

### Practice Worksheets

The practice sheets follow the same topic pattern as the practice sheets.

- Practice 1 - What is the inverse of the following matrices?
- Practice 2 - You can express the determinant of a 2 x 2 matrix as: l A l = ad - bc .
- Practice 3 - I wish I could have used this method in some physics applications.

### Math Skill Quizzes

I used small numbers to make sure that they can focus on the concept, not the calculations.

- Quiz 1 - Determinants help us predict theoretical outcomes and results.
- Quiz 2 - The applications of this form of math is more geared toward theory.
- Quiz 3 - Now we will calculate by using this method.

### What are Determinants and Inverses of Matrices?

Matrices are a rectangular array of data that is organized into rows and columns. The data that is compiled within in them is used for all different types of statical analysis to help people make better decisions. They also have a great deal of use in geometric analysis to calculate precise locations of everything. Self-driving vehicles heavily rely on this form of math to make sure that they are travelling accurately and safely.

The determinant is a scaler value of a squared matrix which encodes specific properties of the linear transformation. It helps us determine the inverse of a matrix which can be helpful in many linear and calculus-based situations. As we alluded to before, this can only be applied to symmetrical matrices (same number of rows and columns). To find the determinant value of a 2 x 2 matrix is, you can multiply the 1st and 3rd element and 2nd and 4th element. Now, you must subtract the previous one with the latter one. In some cases, you will be forced to expand from the third row. That means, we placed a pointer on each element of the row and neglected all elements above it and on its side(s). Not to mention that before the second element, the sign is minus. So, if the element has a minus sign of its own, then the signs will cancel each other out.

The inverse of a matrix is basically a reciprocal or one over the value. When you multiply a matrix by its inverse, we get an Identity Matrix. These come in handy because we cannot divide a matrix. Instead, we multiple the inverses of them which accomplishes the same outcome. This may not seem like a skill that you would use very often, but real-world cryptography heavily relies on the use of this to encrypt and decrypt information.