Let T: P3 (IR) –→ R² is given by T(p) = (p"(0),p'(0). (a) Calculate [T where a and B are the standard bases for P (R) and R². 3 (b) Find bases for N (T) and R(T). (c) Compute the nullity and rank for...

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Extracted text: Let T: P3 (IR) –→ R² is given by T(p) = (p"(0),p'(0). (a) Calculate [T where a and B are the standard bases for P (R) and R². 3 (b) Find bases for N (T) and R(T). (c) Compute the nullity and rank for T. (d) Determine if T is one-to-one, or onto.