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  3. let t : p3(r) ? p4(r) be defined by t(f(x)) = 5f?(

Let T : P3(R) ? P4(R) be defined by T(f(x)) = 5f?(x)-? f(t)dt (integral from 0...

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Advance Math

Let T : P3(R) ? P4(R) be defined by T(f(x)) = 5f?(x)-? f(t)dt(integral from 0 to x)

1. Show that T is a linear transformation.

2.Find dim (P3(R)) and dim (P4(R)).

3.Find rank(T). Find nullity(T)
4. Is T one-to-one? Is T onto? Justify your answers.

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