Mathematics, 23.10.2020 14:00 moneytt2403
2. Let F be the vector space of continuous functions f : R. R and let H be the subspace of F spanned by {1, sin(t), cos(t), cos(20). (a) (Spt) Let K be the set of functions K = sin2(t) + boos2(t) : a, b E R}. Determine whether K is a vector subspace of H or not. (Hint: some standard trigonometric identities could be useful.) Justify your answer. (b) (Spt) Let L be the set of functions L = {sin(t) + a cos(2t) : a E R}. Determine whether L is a vector subspace of H or not. Justify your answer. (c) (Spt) Consider R as a real vector space (under the usual real number addition and multiplica-tion). Let T : H —> R be the function given by T(f) = fir fit) di. Show that T is a linear transformation. (d) (Spt) Find a spanning set for ker(T). Justify your answer. (e) (Spt) Let D : H —> F be given by D(f) = , the first derivative. Show that D is a linear transformation. (f) (Spt) Find a spanning set for ker(D), where D is the linear transformation from part (e). Justify your answer.
Answers: 2
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There are 18 female students and 16 male students in a class. which of the following expresses the ratio of female students to male students in simplest form? а) 10 b) 9 to 8 c) 8: 9 d)18/16
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Mathematics, 22.06.2019 08:20
I4 – 33r2 – 108 which of the following is equal to the polynomial given above?
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2. Let F be the vector space of continuous functions f : R. R and let H be the subspace of F spanned...
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