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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.
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