Let T : Pn → R be defined by T(p(x)) = the sum of all the...

Let T : Pn → R be defined by T(p(x)) = the sum of all the the coefficients of p(x). Show that T is a linear transformation with dim(ker T) = n and conclude that {x − 1, x2 − 1, . . . , x^n − 1} is a basis of ker T.

Expert Solution

milcah answered 2 years ago

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

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