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Homework Help: Linear transformation

  1. Apr 6, 2006 #1
    Find a linear transformation with the given properties

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

    we need to find an expression for t(x,y)
    so we could find what linear combo on (2,-1) and (1,1) yierlds x,y
    But i tried that and i find that i cannot solve this system of linear equations with a consistent solution
    2a + b = x
    -a + b = y
    it doesnt work...

    Please help!
  2. jcsd
  3. Apr 6, 2006 #2
    really? show what you've done so we can see what went wrong.
    Last edited: Apr 6, 2006
  4. Apr 6, 2006 #3
    It is enough to find a linear combination of (2,-1) and (1,1) that eliminates one of the components:
    (2,-1) - 2(1,1) = (0,-3)
    This should tell you how T acts on (0,1) and hence (0,y).
    You can do the same for the other component.
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