# Add, Subtract, and Multiply Matrices Worksheets

We work on applying these operations to matrices. If we remember back a matrix is just a way of organizing data into rows and columns. This is helpful because it provides us an easy means to manipulate, use, and make sense of the data. You can only apply these operations to two matrices that are the same dimensions. If you try to perform these operations on differing size matrices, the results will be classified as undefined. These worksheets and lessons show you how to perform basic operations with matrices. We fill that division does require its own topic and that why you see the topic in the Numbers and Quantity section.

### Aligned Standard: HSN-VM.C.8

- Matrix Differences Step-by-step Lesson- Find the missing number in a basic matrix subtraction problem.
- Guided Lesson - We do all three skills with matrices on this one.
- Guided Lesson Explanation - As you probably guessed the product requires a lot more explanation that sums and differences of matrices.
- Practice Worksheet - Ten problems all in the missing number format to give students a reference when learning the skill.
- Matching Worksheet - Match the missing number to the question mark in the matrix.
- Multiplication Matching Worksheet - This one specifically works on matrices multiplication.
- Multiply a Matrix by a Number Five Pack - This is what happens when matrices and whole number collide.
- Multiplication of Matrices Five Pack - Straight up products for you to play with.
- Solve the Matrix Equation Five Pack - Just find your bearings with the first one and then advance on.
- Addition of Matrices Five Pack - Find the sums of the various sized matrices.
- Subtraction of Matrices Five Pack - Differences always are more fun than sums.

- Answer Keys - These are for all the unlocked materials above.

### 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.

### How to Add, Subtract, and Multiply Matrices?

Performing basic mathematical 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. This is how a great deal of our data is stored in modern databases in all types of real-world applications. The size of the matrix is written in the form of rows (left to right) x columns (up to down). Each position within those row and columns is referred to as an element. 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 (rows or columns) 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. It should be noted that in order to find the sum of two matrices, they must have the same dimensions. If you attempt to find the sum of two matrices of different dimensions, the sum will be undefined.

**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. The same holds true here and this operation can only be performed on matrices with the same dimensions.

**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.