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Let PN denote the vector space of all polynomials of degree N or less, with real...

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Advance Math

Let PN denote the vector space of all polynomials ofdegree N or less, with real coefficients. Let the lineartransformation: T: P3 --> P1 be the secondderivative. Is T onto? Explain. Is T one-to-one? What is the Kernelof T? Find the standard matrix A for the linear transformation T.Let B= {x+1 , x-1 , x2+x , x3+x2 }be a basis for P3 ; and

F={ x+2 , x-3 } be a basis for P1 . Find AF<--B ( the matrix for T relative to the bases B andF).

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