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 EV. Find the matrix A associated to T with respect to the basis (cos(t), sin(t)). A = (T(f))(t) = f'(t) + 7f' (t) + 9f (t),

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A: The solution is given as

Q: Find the domain of the vector-valued function. r(t) = n(t) 0 (-∞, +∞0) O (1, + ∞ ) O (0, +∞ ) O [1,…

A: Find the domain for all three components and then take intersection of those.

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Q: Determine whether the vector functions, x1(t)= [ et ]           [ -et ] and x2(t)= [ et ]…

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Q: 2. Consider the vector-valued function R(t) = { Show that is continuous at t = 1. (el-¹, 1-², In (2-…

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A: Given: Let c1(t)=e5ti+7sintj+t4k and c2(t)=e-5ti+5cos(t)j-7t4k. To Find:      ddt[c1(t)+c2(t)]

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A: Given that c1(t) = e5ti + 7sin(t)j + t4kc2(t) = e-5ti + 3cos(t)j -4 t4k

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Q: Let r(t)= Determine the interval(s) on which this vector valued function is continuous.

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Q: Let r(t) = ⟨t, t, t⟩. Compute r'(t) and interpret the result.

A: rt=t, t, t

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