# Homework Help: Spanning set

1. Apr 30, 2010

### Dustinsfl

If x1, x2,..., xn span $\mathbb{R}^n$, then they are linearly independent.

This is true since n-1 vectors can't span R^n.

How can this be written in a more meaningful way?

2. Apr 30, 2010

### Squeezebox

$\mathbb{R}^n$ is an n-dimensional vector space. {x1,x2,...,xn} is a spanning set of $\mathbb{R}^n$ of length n. This makes {x1,x2,...,xn} a basis of $\mathbb{R}^n$, which means it must be linearly independent.