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let T:P2→P4 be a linear transformation defined by T(a+bx+cx2)=2bx−cx2−cx4. (a) Find ker(T) and give a basis...

let T:P2→P4 be a linear transformation defined by

T(a+bx+cx2)=2bx−cx2−cx4.

(a) Find ker(T) and give a basis for ker(T).

(b) Find range(T)range(T) and give a basis for range(T).

(c) By justifying your answer determine whether T is one-to-one.

(d) By justifying your answer determine whether T is onto.

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