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Linear Transformations question

  1. Nov 16, 2005 #1
    I'm just wondering if someone can let me know if i'm on the right path here...

    this question asks to show that the Function T: R^3 ----> R^2 given by the formula T(X1, X2, X3) = (2X1 - X2 + X3, X2 - 4X3) is a linear transformation.

    soln' the definition of a L.T. is that T(u + v) = T(u) + T(V)

    and T(cU) = cT(U)

    so i show that T[(X1, X2, X3)+(Y1, Y2, Y3)] = T(X1, X2, X3) + T(Y1, Y2, Y3)....but what do i use as Y1, Y2, Y3? thanks for the time and help
  2. jcsd
  3. Nov 16, 2005 #2


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    Just leave them like that. Using the definition of T, write out explicitely what T[(X1, X2, X3)+(Y1, Y2, Y3)] is, and write explicitely what T(X1, X2, X3) + T(Y1, Y2, Y3) is, and then compare.
  4. Nov 16, 2005 #3
    but what happens to (2X1 - X2 + X3, X2 - 4X3)?? do i just write the X's as Ys?
  5. Nov 17, 2005 #4


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    If f(x)= x2, what is f(y)?
  6. Nov 17, 2005 #5
    y as in yes, i got it!
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