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Linear Transformation

  1. Feb 8, 2008 #1
    [SOLVED] Linear Transformation

    1. The problem statement, all variables and given/known data
    Determine if this is a linear transformation:

    L(x,y) = (x+1, y, x+y)


    2. Relevant equations

    This is just one, but I have no clue as to how to even begin. I've been to lecture and read the book over and over again, but i was not given any relevant examples. Could someone please walk me through this? I know that to show it is a linear transformation, i must show that L(u+v) = L(u) + L(v), but i cant seem to find L(u+v)


    3. The attempt at a solution

    u =
    [x
    y]

    v =
    [x'
    y']

    L(u) + L(v) =
    x + x' + 2
    y + y'
    x + y + x' +y'

    I'm not even sure that is correct, but if it is, how does one find L(u+v)? Additionally, the fact that it is a transformation from R^2 => R^3 is throwing me off
     
    Last edited: Feb 8, 2008
  2. jcsd
  3. Feb 8, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    The domain is R^2, they mean that (x,y)+(x',y') should be defined by (x+x',y+y'). What's L of that?
     
  4. Feb 8, 2008 #3
    would L(x+x', y+y') = x+x'+2 ???
    y+y'
    x+1+y

    It's probably extremely obvious, but i still dont understand.
     
  5. Feb 8, 2008 #4

    Dick

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    Science Advisor
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    L(x+x',y+y') would be (x+x'+1,y+y',x+x'+y+y'). Look at the definition. Substitute x+x' -> x and y+y' ->y. Notice that's different from what you found for L(u)+L(v).
     
  6. Feb 9, 2008 #5
    ah that makes sense! I think i understand now.Thx for the help!
     
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