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.
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.
Don't worry! Each sheet is successively more difficult. The first sheet is a bit too simple.
Math Skill Quizzes
The answers here label the exact values to help you check your answers.