# How do you perform scalar multiplication with vectors?

Jun 2, 2018

Multiply each component by said scalar

#### Explanation:

Given a vector $v$ of any dimension:

$v = \left({v}_{1} , {v}_{2} , \ldots , {v}_{n}\right)$

The multiplication between $v$ and any scalar $\lambda$ is defined as

$\lambda v = \left(\lambda {v}_{1} , \lambda {v}_{2} , \ldots , \lambda {v}_{n}\right)$

For example, if $n = 3$ and you consider $v = \left(1 , 4 , - 6\right)$ and $\lambda = 2$ you have

$\lambda v = 2 v = \left(2 , 8 , - 12\right)$