Let V be the subspace of the vector space of continuous functions on R spanned by the functions cos(t) and sin(t). Consider the linear transformation T: V→ V given by for f € V. Find the matrix A associated to T with respect to the basis (cos(t), sin(t)). A = (T(ƒ))(t) = ƒ"(t) + 6ƒ' (t) + 8 f(t),

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Chapter2: Second-order Linear Odes
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Let V be the subspace of the vector space of continuous functions on R spanned by the functions cos(t) and sin(t).
Consider the linear transformation T: V→ V given by
for f € V.
Find the matrix A associated to T with respect to the basis (cos(t), sin(t)).
A =
(T(ƒ))(t) = ƒ"(t) + 6ƒ' (t) + 8 f(t),
Transcribed Image Text:Let V be the subspace of the vector space of continuous functions on R spanned by the functions cos(t) and sin(t). Consider the linear transformation T: V→ V given by for f € V. Find the matrix A associated to T with respect to the basis (cos(t), sin(t)). A = (T(ƒ))(t) = ƒ"(t) + 6ƒ' (t) + 8 f(t),
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