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Vectors in 4-space. HELP?

  1. Feb 4, 2009 #1
    The problem statement, all variables and given/known data

    Find three vectors in R^4 (none of which are the zero vector) such that they are linearly dependent and v3 is not in the Span of v1&v2.

    The attempt at a solution

    My answer was v1=[1,0,0,0] v2=[0,1,0,0] & v3=[0,0,1,0]

    Does this work? v3 is not in the span of v1&v2. If placed in a matrix set equal to zero, there is a free variable x4. So aren't they linearly dependent?
  2. jcsd
  3. Feb 4, 2009 #2


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    Science Advisor
    Homework Helper

    No, they are linearly independent. c1*v1+c2*v2+c3*v3=0 has c1=c2=c3=0 as it's only solution. Nothing in the problem said v1 and v2 have to be linearly independent.
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