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
- 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.
- 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.
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.