(d) (2 points) If T is a linear transformation from P (the vector space of all polynomials) to S (the vector space of al
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(d) (2 points) If T is a linear transformation from P (the vector space of all polynomials) to S (the vector space of al
(d) (2 points) If T is a linear transformation from P (the vector space of all polynomials) to S (the vector space of all sequences), that takes a polynomial ao +12+...+2,2" to a sequence of its coefficients do, a1,..., An,0,0,0,.... What is the kernel of T? (e) (2 points) Is the set of smooth functions {1, sinº (x), sin(x), cos? (x)} a linearly inde pendent set? WHY or WHY NOT? (f) (2 points) Let V be some vector space of dimension n. A spanning set S of V contains n elements. Is S linearly independent? WHY or WHY NOT?
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