Question: 5. 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

5. 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, . . . , xn 1} is a basis of ker T

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