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Making a set a basis

  1. Feb 18, 2008 #1
    Ok, so I have the set S={cosx^2, sinx^2, cos(2x)} that spans V.

    So obviously this is not a basis. Because the third is a linear combination of the first; ie. cosx^2-sinx^2=cos(2x). But if I were to take the first 2 vectors, would they span V? That is does the equation a(cosx^2)+b(sinx^2)=0 imply a=0& b=0?
  2. jcsd
  3. Feb 18, 2008 #2

    George Jones

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    Do you mean: Are the first two vectors linearly independent?

    Use [itex]\cos^2x = 1 - \sin^2x[/itex].
  4. Feb 18, 2008 #3


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    try evaluating at x=0 and x=[itex]\pi/2[/itex]
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