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

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.

Expert Solution

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Colby Messinger answered 2 years ago

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

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