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Linear algebra - change of basis matrix

  1. Jan 30, 2010 #1
    1. The problem statement, all variables and given/known data

    Let A = {(1, 1), (2,0)} and B = {(0, 2), (2, 1)} in R2.
    a) Find A (u with respect to A) if B = [3, -2].

    2. Relevant equations



    3. The attempt at a solution

    I tried to find AB (transition matrix from B to A), then apply to B, but couldn't represent (2, 1) with respect to A?

    So I found u by BB = u,
    then u = (4, -4).

    Now represent u with respect to A:
    A = (-4, 4)

    Is this correct?
     
  2. jcsd
  3. Jan 30, 2010 #2
    Yes, that's how it's done. You don't need to bother too much.
    We know that _B=[3,-2]^t => u=3*(0,2)-2*(2,1)=(-4,4).
    Now, in order to find _A we need to find a,b in R such that :
    a*(1, 1)+b*(2,0)=(-4,4) => a+2b=-4 and a=4 => a=4 and b=-4.
    Therefore : _A = [4,-4]^t.
    DONE! :)
     
    Last edited: Jan 30, 2010
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