Home > Grade Levels > High School Numbers and Quantity >

## Add, Subtract, and Multiply Matrices

#### High School - HSN-VM.C.8

How to Add, Subtract, and Multiply Matrices? Operations on matrices is a relatively easier concept. However, it requires precision and keen focus to learn to solve them. A matrix is an array of numbers, with a set of rows and columns. Let's deal with all three operations individually. Addition - The addition is the most straightforward operation, given that you only have to match the position of elements to solve them. You would add the matching positions within the matrices and find their sum. For instance, if you are adding two (2 x 2) matrices, add the value of the upper lefts together, then move to upper right, and so on. Subtraction - Subtraction is similar to addition, where you need to match the position of elements and find the difference they are placed right where they are located. Multiplication - Two multiply two matrices, we don't look at the position of the elements alone. Moreover, you cannot multiply every matrix. For matrix multiplication, you need to fulfil a condition, i.e. m × n × n × p, where all the alphabets represent rows and columns of the matrices. Here, both n should be equal for multiplication to work. After proving the condition, multiply both matrices, you need to do dot product. In other words, you have to multiply the first row of the first matrix with each column of the second matrix and then multiply the next row similarly and so on. Let us solve an example. These worksheets and lessons show you how to perform basic operations with matrices. We fill that division does require it's own topic and that why you see the topic in the Numbers and Quantity section.

### Printable Worksheets And Lessons  #### Homework Sheets

What is missing from your matrix?

• Homework 1 - When subtracting two matrices, we find the difference between numbers in the same column and row.
• Homework 2 - We go over both addition and subtraction.
• Homework 3 - To remember how to multiply two matrices, first imagine the two matrices with the second matrix moved up.

#### Practice Worksheets

Each sheet focuses on a different operation. We didn't mix them up, so you can work on one at a time.

• Practice 1 - Fill in the missing number in these subtraction problems.
• Practice 2 - A mix of operations can be found here.
• Practice 3 - This one is a little more bold in typeface for printing purposes.

#### Math Skill Quizzes

Most of the problems are looking for the finished sum, difference, or product of the matrices.

• Quiz 1 - In this case, we need to find a missing number that comes after the addition of the entries of the same row and column of the left-hand matrices.
• Quiz 2 - Find the sum between two matrices.
• Quiz 3 - There is a formula for multiplying matrices that we previously reviewed with you.