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Homework Help: Liear transformation

  1. Mar 15, 2009 #1
    1. The problem statement, all variables and given/known data
    Determine whether the following maps are linear transformations
    a) L: R^2 -- R
    x1^2 +x2^2
    b) L: Mn*n(R)--Mn*n(R)
    A-- A-A^T
    c)L:P3--P2 f-- f'+(f(3))t^2

    2. Relevant equations

    3. The attempt at a solution
    I have to show L(x+y)=L(x)+L(y) and cL(X)=L(cx)
    for a) i find that (x1+y1)^2+(x2+y2)^2 not equals to (x1+x2)^2+(y1+y2)^2
    so it isn't a linear transformaton
    for b) can i use the counterexample
    because A=A^T
    for c) no idea for this one
    Last edited: Mar 15, 2009
  2. jcsd
  3. Mar 15, 2009 #2
    b) L(A)=0, but that does not mean that L is not linear.

    c) You know how elements of P3 look like: at^3+bt^2+ct+d. Check if linearity holds: L(v+w)=L(v)+L(w), L(rv)=rL(v) where you take for v and w elements of P3.
  4. Mar 15, 2009 #3
    so how can i get a counterexample for b) ?
  5. Mar 15, 2009 #4
    Try proving linearity instead. :wink:
  6. Mar 15, 2009 #5
    thx . i will try it
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