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Math Help - Lin. Transformation

  1. #1
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    Lin. Transformation

    Let T be the Lin. Trans. p_2 \rightarrow p_2 defined by

    T(at^2+bt+c) = (3a+2c)t + (2b-5c)

    1.) Determine a basis of the kernel of T

    2.) Determine a basis of the range of T

    3.) Is T onto? Is T one-to-one? Explain!


    ....

    Well for #3 I know one-to-one has to do w/ range and onto has to do w/ kernel...

    Some help?
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  2. #2
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    Quote Originally Posted by caeder012 View Post
    Let T be the Lin. Trans. p_2 \rightarrow p_2 defined by

    T(at^2+bt+c) = (3a+2c)t + (2b-5c)

    1.) Determine a basis of the kernel of T

    2.) Determine a basis of the range of T

    3.) Is T onto? Is T one-to-one? Explain!


    ....

    Well for #3 I know one-to-one has to do w/ range and onto has to do w/ kernel...

    Some help?
    Is the basis of the kernel basis = span{ -4t^2 + 15t + 6}

    because those coefficients make (3a+2c) + (2b- 5c) = 0

    And for range.. range = span {  t + 1}

    Hmm..
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  3. #3
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    Quote Originally Posted by caeder012 View Post
    Is the basis of the kernel basis = span{ -4t^2 + 15t + 6}

    because those coefficients make (3a+2c) + (2b- 5c) = 0

    And for range.. range = span {  t + 1}

    Hmm..
    Anyone have some insight? One of the hardest lin alg problems I've come across.
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  4. #4
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    Shouldn't you be thinking about:

    3a + 2c = 0

    AND

    2b - 5c = 0

    ????

    You certainly found one solution to this over-defined system. What about the infinitely many others?

    May 'a' be zero (0)?
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