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Linear Transformation

  1. Nov 17, 2008 #1
    1. The problem statement, all variables and given/known data

    T: R3 --> R2 by T(x,y,z) = (z-x , 2y -x)
    v = (2, -1, -3)
    B = {(0,0,1),(0,1,1),(1,1,1,)}
    C = {(1,-1), (2,1)}

    What is [T]BC
    what is [v]B
    and what is T(v)

    2. Relevant equations

    No clue

    3. The attempt at a solution

    I found out [T]B and that's where i am stuck.
  2. jcsd
  3. Nov 17, 2008 #2


    Staff: Mentor

    I'm pretty sure that [tex][T]_{BC}[/tex] is the matrix representation of T on the vectors in B, in terms of the basis vectors in C.

    For example, T(b1) = T(0,0,1) = (1,0)
    In terms of the basis in C, this is 1/3 (1, -1) + 1(2,1)

    So the first column of [tex][T]_{BC}[/tex] is (1/3, 1) (written as a column vector).
    You need to do this for the other two vectors in B.

    [tex]v_B[/tex] is the representation of v in terms of the basis B.
    T(v) is pretty straightforward.
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