## Unique Properties of Matrix Operations

#### Aligned To Common Core Standard:

**High School** - HSN-VM.C.9

Unique Properties of Matrix Operations -
Like every other concept in mathematics, matrices hold some unique and special properties too. But surprisingly matrices have a whole set of unique properties which makes them hold a special position in mathematics. To completely understand what matrices, entail as their unique operations, learn about the following unique operations of matrices:
**Properties involving Addition:** - Consider A, B, and C be matrices. Therefore;
1. A+B = B+A 2. (A+B) + C = A + (B+C) 3. A+O = A, where O is the matrix (m x n) which is zero-matrix. 4. A + B = O, if B = - A.
**Properties involving Multiplication** - Consider a, b and c be three matrices. If the products of AB, (AB) C, BC, and A (BC) are valid, then we have: (AB) C = A (BC)
If α and β are numbers, and A is a matrix, then we have:
1. α (βA) = ( α β)A 2. α (AB) = ( αA)B = A( αB) **Properties involving Addition and Multiplication** - Let A, B and C be three matrices. If the products of AB, BC and AC are valid, then we have:
1. (A+B)C = AC + BC and 2. A(B+C) = AB + AC 3. α (A+B) = αA + βB and 4. ( α +β) A = αA + βa . These lessons and worksheets look at many different properties of operations and how to apply those directly toi matrix operations.

### Printable Worksheets And Lessons

- Finding Dimensions Step-by-step Lesson- What are the dimensions of this matrix operations series.

- Guided Lesson - A triple sum, difference, and mix operations with matrices.

- Guided Lesson Explanation - This skill is easier than it first looks. It has a lot of applications though.

- Practice Worksheet - We stress you on all levels with this matrix problem set.

- Matching Worksheet - I made one of each type of problem for this standard.

#### Homework Sheets

We really start to classify and breakdown what a matrix is.

- Homework 1 - Multiplying a matrix by a number does not change its dimensions. A is the difference of the matrices that have 1 row and 2 columns.
- Homework 2 - All the three matrices being added have 3 rows and 1 column, so their sum B also has 3 rows and 1 column.
- Homework 3 - Since the two matrices do not have the same number of columns, their difference is not defined.

#### Practice Worksheets

Don't worry! Each sheet is successively more difficult. The first sheet is a bit too simple.

- Practice 1 - What are the dimensions of matrix A? A = 3[7 2] - [3 4]
- Practice 2 - What are the dimensions of matrix B?
- Practice 3 - The first matrix has 2 rows and 2 columns and the second matrix has 2 rows and 3 columns.

#### Math Skill Quizzes

The answers here label the exact values to help you check your answers.