Mathematics, 07.12.2020 17:30 shatj960
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 β> 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 β> 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: 3
Mathematics, 21.06.2019 20:30
William invested $5000 in an account that earns 3.8% interest, compounded annually. the formula for compound interest is a(t) = p(1 + i)t. how much did william have in the account after 6 years? (apex)
Answers: 2
Mathematics, 21.06.2019 22:20
The four students in the table below each recorded the time and distance traveled while exercising. exercising distance (miles) time (minutes) gia 2 30 harris 5 50 ian 3 40 jackson 4 80 which list ranks the students from fastest walker to slowest walker? jackson, gia, ian, harris harris, jackson, ian, gia harris, ian, gia, jackson jackson, harris, ian, gia
Answers: 3
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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