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Homework Help: Linear transformation

  1. Feb 8, 2010 #1
    1. The problem statement, all variables and given/known data
    T : U -> V is a linear map defined by
    T(a,b) = (a-b,a+b)
    write down the matrix T using the standard basis of R^2

    2. Relevant equations



    3. The attempt at a solution
    basis of V = { (1,1) , (-1,1) }

    standard basis of R^2 is (1,0) and (0,1)
    and the matrix T is essentially ( T(1,0) T(0,1) ) right? where T is a 2x2 matrix
    but I don't know how to evaluate T(1,0) and T(0,1)...
     
  2. jcsd
  3. Feb 8, 2010 #2

    HallsofIvy

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  4. Feb 8, 2010 #3
    oh yeah! oops

    say if the basis given are (-1,1) and (0,-2)
    what I get for matrix T is

    T(-1,1) = (-1-1,-1+1) = (-2,0)
    T(0,-2) = (0-(-2),0+(-2) = (2,-2)

    so T is (-2, 0
    2, -2 )

    but when I multiply it with (a,b) to its RHS, I don't get (a-b,a+b)
     
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