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Math Help - Linear Transformations

  1. #1
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    Linear Transformations

    Can someone help me with the following problem. I'm not getting this at all.

    Determine whether the function is a linear transformation:
    T: R^2 -> R^2, T(x,y) = (x,1)
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  2. #2
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    Quote Originally Posted by larson View Post
    Can someone help me with the following problem. I'm not getting this at all.

    Determine whether the function is a linear transformation:
    T: R^2 -> R^2, T(x,y) = (x,1)
    it's not because T(0,0) \neq (0,0).
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  3. #3
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    Quote Originally Posted by NonCommAlg View Post
    it's not because T(0,0) \neq (0,0).
    Could you by any chance show this further by using the two rules of linear transformations, which are:
    1. T(u + v) = T(u) + T(v)
    2. T(cu) = cT(u)

    I appreciate what you gave me so far though.

    Larson
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  4. #4
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    Quote Originally Posted by larson View Post
    Could you by any chance show this further by using the two rules of linear transformations, which are:
    1. T(u + v) = T(u) + T(v)
    2. T(cu) = cT(u)

    I appreciate what you gave me so far though.

    Larson
    By rule #2 if you let c=0 then you get T(\bold{0}) = \bold{0}.
    Thus, every linear transformation must satisfy this property.
    But it does not.
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