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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Originally Posted by skittle 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.
A generic P4 would look like a4x^4+a3x^3+a2x^2+a1x+a0. How would I then apply the transformation?
Originally Posted by skittle 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).
So I would make the x's to be zeros?
Originally Posted by skittle So I would make the x's to be zeros? Find the second derivative, then plug in zero.
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