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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

3 columns2 rows[255267]
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 A=[10643], let's find 2A.
To find 2A, simply multiply each matrix entry by 2:
2A=2[10643]=[210262423]=[201286]

Check your understanding

Problem 1
Given B=[4271], find 3B.
3B=

Problem 2
Given C=[42273], find 13C.
13C=