## Multiply Matrices by Scalars to Produce New Matrices

#### Aligned To Common Core Standard:

**High School** - HSN-VM.C.7

How to Multiply Matrices by Scalars?
An array of numbers that are arranged in a rectangular form is what we call a matrix. 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!
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

Consider an example; 2 × (2/6 x 4/8) = (4/12 x 8/16). This selection of worksheets explores how to manipulate matrices multiplication by using scalars.

### Printable Worksheets And Lessons

- 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.

#### 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.