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Math Help - Linear transformation

  1. #1
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    Linear transformation

    How do you find a basis for Ker(φ), a basis for Im(φ), the dimensions of the kernel, image and domain of φ for the following linear transformation.

    φ : P4 -> R given by φ(p(x)) = p′′(0), where p′′(x) denotes the second derivative
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  2. #2
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    Quote Originally Posted by skittle View Post
    How do you find a basis for Ker(φ), a basis for Im(φ), the dimensions of the kernel, image and domain of φ for the following linear transformation.

    φ : P4 -> R given by φ(p(x)) = p′′(0), where p′′(x) denotes the second derivative
    What would a generic P4 polynomial look like? Then apply the transformation.
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  3. #3
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    A generic P4 would look like a4x^4+a3x^3+a2x^2+a1x+a0. How would I then apply the transformation?
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  4. #4
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    Quote Originally Posted by skittle View Post
    A generic P4 would look like a4x^4+a3x^3+a2x^2+a1x+a0. How would I then apply the transformation?
    By what you wrote, it says take p''(0).
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  5. #5
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    So I would make the x's to be zeros?
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  6. #6
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    Quote Originally Posted by skittle View Post
    So I would make the x's to be zeros?
    Find the second derivative, then plug in zero.
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