# Math Worksheets Land

Math Worksheets For All Ages

# Math Worksheets Land

Math Worksheets For All Ages

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# Unique Properties of Matrix Operations Worksheets

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.

### Aligned Standard: HSN-VM.C.9

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

### 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.