# Matrices

Scalar Multiplication

# At a Glance - Scalar Multiplication

## Scalar Multiplication: One is the Loneliest Scalar?

Multiply matrices by scalars to produce new matrices, for example, when all of the payoffs in a game are doubled.

We know what you're thinking. What the heck is a scalar? Scalar is a fancy-panties way of saying number. By number we mean any of these things:

You can multiply any of these babies through a matrix with ease. Take this matrix:

Her name is S. We need to find 3S. Here's how that looks:

3S is really just 3 multiplied through the matrix:

So

Moving on, there are more complicated examples of scalar multiplication. For example, we already know our matrix, S. This one is K:

How do we find this?

2K + S

Basically, we just plug the matrices in for their variables and go:

We multiply the 2 through the K matrix first:

Then we're ready to just add the two matrices. We remember how to do that, of course; we just add the entries in each location:

As long as your matrices are the same size for addition and subtraction purposes, it's all good.

#### Example 1

 Find the product:

#### Example 2

 Find the product:

#### Example 3

 Find the product:

Find CD.