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## Algebra (all content)

### Course: Algebra (all content)>Unit 20

Lesson 6: Multiplying matrices by scalars

# Multiplying matrices by scalars

Learn how to find the result of a matrix multiplied by a real number.

## What you should be familiar with before taking this lesson

$\begin{array}{c} \goldE{\text{3 columns}} \\\\ \begin{array}{c} \blueE{\text{2 rows}}&\goldE{\LARGE\downarrow}&\goldE{\LARGE\downarrow}&\goldE{\LARGE\downarrow} \\\\ \begin{array}{c} \blueE{\LARGE\rightarrow} \\\\ \blueE{\LARGE\rightarrow}\end{array} &\left[\begin{array}{c} -2 \\\\ 5\end{array}\right. &\begin{array}{c}5 \\\\ 2\end{array} &\left.\begin{array}{c}6 \\\\ 7\end{array}\right] \end{array} \end{array}$
A matrix is a rectangular arrangement of numbers into rows and columns. Each number in a matrix is referred to as a matrix element or entry.
If this is new to you, you might want to check out our intro to matrices. You should also make sure you know how to add and subtract matrices.

## What you will learn in this lesson

We can multiply matrices by real numbers. This article explores how this works.

## Scalars and scalar multiplication

When we work with matrices, we refer to real numbers as scalars.
The term scalar multiplication refers to the product of a real number and a matrix. In scalar multiplication, each entry in the matrix is multiplied by the given scalar.
For example, given that $\bold A=\left[\begin{array}{c} 10 &6 \\\\ 4& 3 \end{array}\right]$, let's find 2, A.
To find 2, A, simply multiply each matrix entry by 2:
\begin{aligned} \greenD 2\bold A&=\greenD{2}\cdot{\left[\begin{array}{c} 10 &6 \\\\ 4& 3 \end{array}\right]} \\\\ &={\left[\begin{array}{c} \greenD2 \cdot10 &\greenD2\cdot 6 \\\\ \greenD2\cdot 4& \greenD2\cdot3 \end{array}\right]} \\\\ &=\left[\begin{array}{c} 20 &12 \\\\ 8& 6 \end{array}\right] \end{aligned}

Given $\bold B=\left[\begin{array}{c} -4 &-2 \\\\ 7& 1 \end{array}\right]$, find minus, 3, B.
Given $\bold C=\left[\begin{array}{c} -42 \\\\ 27 \\\\ -3 \end{array}\right]$, find start fraction, 1, divided by, 3, end fraction, C.