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Unique Properties of Matrix Operations

HSN-VM.C.9
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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




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.

  • Quiz 1 - We focus on differences here.
  • Quiz 2 - Both matrices being added have 3 rows and 1 column, so their sum B also has 3 rows and 1 column.
  • Quiz 3 - Since the two matrices do not have the same number of columns, their difference is not defined.