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### Course: Precalculus > Unit 7

Lesson 3: 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

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 $\mathbf{A}=\left[\begin{array}{cc}10& 6\\ \\ 4& 3\end{array}\right]$ , let's find $2\mathbf{A}$ .

To find $2\mathbf{A}$ , simply multiply each matrix entry by $2$ :

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