## Table of Contents

- Matrix Math
- Matrix Notation
- Equal Matrices
- Addition of Matrices
- Subtraction of Matrices
- Multiplication of Matrices
- Division of Matrices
- Lesson Summary

- FAQs
- Activities

## Additional Matrix Operation Examples

In the following examples, students will apply their knowledge of addition, subtraction, and multiplication of matrices to determine various sums, differences, and products. Some problems will use only one operation whereas others will combine operations.

## Examples

For the following matrices,

determine the following, if they exist.

1) A + E

2) B - C

3) DE

4) ED

5) (A + E)B

6) (A - E)C

## Solutions

1) Since A and E are the same size (they are both 3x2 matrices), we can add them by adding their corresponding elements.

2) We cannot calculate B - C because the matrices are not the same size.

3) We can calculate DE because the number of columns of D matches the number of rows of E.

Remember to multiply a row of D by a column of E. For example, the first entry in the product is found by multiplying the first row of D by the first column of E to get 3(2) + 2(0) + 6(1) = 6 + 0 + 6 = 12.

4) We cannot calculate ED because the number of columns of E (2) does not match the number of rows of D (3). Note that this means that the order of multiplication matters - we could calculate DE but not ED.

5) We found A + E in number 1. We can multiply (A + E) and B because the number of columns of (A + E) matches the number of rows of B.

6) We can subtract E from A because the matrices are the same size. Then, we can multiply (A - E) by C because the number of columns of (A - E) matches the number of rows of C.

#### What is a 2x3 matrix?

A 2x3 or 2 by 3 matrix is a matrix that has 2 rows and 3 columns. Every matrix is referred to by two numbers: the first is the number of rows and the second is the number of columns. Also, 2x3 is called the matrix order.

#### What happens when two matrices are equal?

When two matrices are equal, they become the same matrix and so referring to any of the two is the same as referring to the other one. The same logic applies when referring to n number of equal matrices; any one of them can represent them all.

#### How do you notate a matrix?

Use an upper case letter to notate a matrix. For example writing matrix A is correct while writing matrix a is incorrect. Matrix elements are notated with the lower case version of the matrix name with subscript numbers denoting their row and column position.

#### How do you know if matrices are equal?

For two matrices to be called equal, all of their elements that share the same notations must be equal. This is equal to saying that the element a1,1 from matrix A must be equal to element b1,1 from matrix B and so forth for all corresponding elements from both martices.