# Scalar Multiplication of Matrices Worksheets

This type of operation occurs when you have a fixed matrix which is normal a selection of data that you are analyzing, and you are attempting to amplify or reduce it by a set scale of real numbers. The name “scalar” is used because it refers to changing the vector or matrices without changing its core attributes such as its direction or dimensions. The math behind this is pretty simple. Matrices are a series of data in rows and columns. When you multiply them by a scalar, you simply multiply each value in each row and column by that real number. This selection of worksheets explores how to manipulate matrices multiplication by using scalars.

### Aligned Standard: HSN-VM.C.7

- Missing Number Step-by-step Lesson- A simple matrix multiplied by a whole number. What's the outcome?
- Guided Lesson - We stick very close to the lesson to make these very do-able for kids.
- Guided Lesson Explanation - We also recommend that you review this in fraction based form even though the standards don't directly call for it.
- Practice Worksheet - Some kids will start to see this as straight multiplication which it definitely is not.
- Matching Worksheet - Match the products and the whole numbers and matrices that produced it.

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

### Homework Sheets

Starting with the root definition of a matrix and scalar can help this skill go by quicker.

- Homework 1 - We have to multiply the matrix in order to fill in the missing number.
- Homework 2 - You can work these problems best by breaking it up into components.
- Homework 3 - The missing number is the product of: 6 (8), which is 48.

### Practice Worksheets

A scalar is, for all purposes and intents, just a real number. Matrices are more dynamic.

- Practice 1 - Find the missing number to complete the product of the matrix.
- Practice 2 - We focus on finding unknowns within Matrices.
- Practice 3 - It may seem simple, but wait until we break away from 2 by 2 matrices.

### Math Skill Quizzes

Print these off to see how it all came together for students.

- Quiz 1 - The missing number is in row 2 of column 1.
- Quiz 2 - Here is a lot more practice for you on this.
- Quiz 3 - The original matrix must be multiplied in order to fill in the missing number.

### How to Multiply Matrices by Scalars?

An array of numbers that are arranged in a rectangular form is what we call a matrix. This is a great way to store data and gives you a platform for which you can analyze and/or manipulate it. It is arranged in rows and columns, and the order of a matrix is written as;

**Rows × Columns** - There are a variety of different types of matrices including square matrix, identity matrix, null matrix, zero matrix, and many others. You can apply all basic arithmetic functions on these matrices, such as addition, subtraction, division, and multiplication. There are two different types of multiplication that we can apply on matrices and these include scalar multiplication and matrix multiplications. Scalar multiplication is the simplest form of multiplication. Because you are simply multiply each row or column of data and multiplying it by a fixed value. In a way you are just amplifying all your data across the matrix. Take a look at the most commonly used rectangular array:

Consider a matrix of order 2 × 2;

a b

c d

Now, if you have to multiply it with a scalar quantity (k); you have to multiply the constant with each element of the matrix.

ka kb

kc kd

As you can see, this not that complicated and really just requires that you stay organized throughout the process.