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Linear transformations

  1. Apr 20, 2008 #1
    [SOLVED] Linear transformations

    1. The problem statement, all variables and given/known data

    Determine whether the following maps are linear transformations. (proofs or counterexamples required)

    a.) L: R^2[tex]\rightarrow[/tex]R^2,

    (2x1 + 3x2)

    The brackets should be two large brackets surrounding the two vectors.

    3. The attempt at a solution
    I've been reading about linear transformations and i know i have to show something like:

    L(x1+x2)= L(x1) +L(x2) and L(cx1)= cL(x1) where c is a scalar.

    Is this right and i should treat x1 and x2 separately rather than the vector including x1 and x2 as one element of R^2?

    What im trying to say is, do i need to define a vector (y1, y2) aswell in the set of R^2?
    Last edited: Apr 20, 2008
  2. jcsd
  3. Apr 20, 2008 #2
    For x,y [tex]\in[/tex]R^2,

    x=(x1,x2) and y= (y1,y2)

    x+y=(x1,x2)+(y1,y2)= (x1+y1, x2+y2)
    L(x+y) = L(x1+y1, x2+y2)
    =L(x) +L(y)

    Is this right for the first part?

    Then because cx= c(x1,x2) = (cx1,cx2) you have
    L(cx) = L(cx1, cx2) = (2cx1 + 3cx2)
    =c(2x1 + 3x2)

    I think i'm understanding it more now, if this is right that is.
  4. Apr 20, 2008 #3


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    That's right. I think you've got it.
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