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 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: 2
Mathematics, 21.06.2019 18:40, jesus3426
A33 gram sample of a substance that's used to detect explosives has a k-value of 0.1473. n = noekt no = initial mass (at time t = 0) n = mass at time t k = a positive constant that depends on the substance itself and on the units used to measure time t = time, in days
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Mathematics, 21.06.2019 20:30, jnelso5437
How do you determine if an ordered pair is a solution to a given equation?
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Mathematics, 21.06.2019 21:40, jacobasencio23
Use sigma notation to represent the following series for 9 terms.
Answers: 2
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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