## Null, Identity and Inverse Matrices

#### Aligned To Common Core Standard:

**High School** - HSN-VM.C.10

What are Null, Identity, and Inverse Matrices? (NB)
A matrix represents a rectangular array of numbers arranged in columns and rows. These numbers are known as the entries or elements of the matrix.
The arrangement of elements in rows and columns determine the dimension of a matrix. The dimensions of any matrix are written as 'm x n', where m represents the number of rows, and n represents the number of columns.
There are several different forms of matrix that you should investigate because they will give strategies to use when working to solve them.
**NULL MATRIX** -
The null matrix is the easiest one to identify. If each entry of an m x n matrix is zero, the matrix is said to be the zero or null matrix. It is written as 0_{m, n}.
[0 0] is a null matrix with 1 x 2 dimensions. These come in many different varities and can help you better understand the entire system.
**IDENTITY MATRIX** - A square matrix having all the elements of the main diagonal as 1 with the remaining elements as 0 is known as an identity matrix. Identity matrix is also known as a unit matrix. Identity matrix is denoted by I_{n x n} , where n x n represents the dimensions of the matrix .
**INVERSE MATRIX** - The inverse of a matrix A is a matrix that results in an identity matrix when multiplied by matrix A. inverse of the matrix is denoted by A^{-1}. These worksheets and lessons introduce students to three unique forms of matrices and how to operate with.

### Printable Worksheets And Lessons

- Null Matrix Step-by-step Lesson- Null means zero, students love that one. Good to start them off with confidence.

- Guided Lesson - An identity matrix, confirming or disavowing inverse matrices, and another null matrix for you.

- Guided Lesson Explanation - The first and last one goes quick. The second one takes a bit of time.

- Practice Worksheet - Write a null matrix with fixed orders, make an identity matrix set, and check for inverses of matrices.

- Matching Worksheet - Yeah, I did kind of take the shotgun approach in putting these together. It came out well though.

#### Homework Sheets

Number 1 = Null Matrices, Number 2 = Inverse Matrices, Number 3 = Identity Matrices.

- Homework 1 - Null matrices contain all 0s. In this case, you must write a 3 x 6 matrix. A 3 x 6 matrix contains 3 rows and 6 columns.
- Homework 2 - We have inserted the number from our matrix into this format.
- Homework 3 - The diagonal contains all 1s.The order of 4 means that the identity matrix is a 4 x 4.

#### Practice Worksheets

Same topic pattern as the homework, but we provide a little more explanation here.

- Practice 1 - Write an identity matrix of order 8?
- Practice 2 - Write a null matrix of order: 4 x 6
- Practice 3 - Check whether an inverse exists for the following matrices.

#### Math Skill Quizzes

We made a quiz on each invidual skill rather than mixxing them up.

- Quiz 1 - While this just seems like you are writing zeroes everywhere, it has a real purpose that we will bring to light in the next topic.
- Quiz 2 - Look at spotting inverses here.
- Quiz 3 - An identity matrix is a square matrix where all entries are zeroes except for the top-left to bottom-right diagonal.