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Linear transformation of matrices

  1. Oct 18, 2009 #1
    Sorry for the poor formatting, I keep getting errors with Latex in preview. I'll appreciate anyone who could reformat the question into Latex.

    Let T: R3 -> R2 be defined by T(x, y, z)T = (x +z, y - z)T. Find the matrix of T with respect to the bases B = {(1,1,0)T,(0,1,1)T,(1,0,1)T} and B' = {(1,1)T,(-1,1)T}.

    Here is what I've done. I don't know what's wrong and I'm going crazy because I can't find what's wrong with it. I believe it's my careless mistake, but I've been checking again and again to no avail.

    T(1,0,0)T = (1, 0)T
    T(0,1,0)T = (0, 1)T
    T(0,0,1)T = (0, -1)T

    AT = (1 0 0, 0 1 -1)T
    PB = (1 0 1, 1 1 0, 0 1 1)T
    PB' = (1 -1, 1 1)T

    PB'-1 = 1/2 (1 1, -1 1)T

    PB'-1ATPB = (1 0 0, 0 0 -1)

    T(u1) = T(1,1,0)T = (1, 1)T [tex]\neq[/tex] v1 + 0v2
    T(u2) = T(0,1,1)T = (1, 0)T [tex]\neq[/tex] 0v1 + 0v2
    T(u3) = T(1,0,1)T = (2, -1)T [tex]\neq[/tex] 0v1 + -v2
     
    Last edited: Oct 18, 2009
  2. jcsd
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