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Question description

For polynomials in P2 (i.e polynomials that can be written as p(t)=a0+a1(t)+a2(t^2) where a0, a1, and a2 are scalars), define the transformation: T: P2-->P1 as T(p(t))=p`(t) (p`(t) is the derivative of p(t)). In other words, T acts by taking the derivative, the good old fashion Calculus derivative. First, show that T is a linear transformation. Then determine the kernel of T.

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