1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Spanning set

  1. Apr 30, 2010 #1
    If x1, x2,..., xn span [itex]\mathbb{R}^n[/itex], 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. jcsd
  3. Apr 30, 2010 #2
    [itex]\mathbb{R}^n[/itex] is an n-dimensional vector space. {x1,x2,...,xn} is a spanning set of [itex]\mathbb{R}^n[/itex] of length n. This makes {x1,x2,...,xn} a basis of [itex]\mathbb{R}^n[/itex], which means it must be linearly independent.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook