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),

(a) Let vt) be a differentiable vector valued function of t. If v. dy = 0 for all t, can we say anything about |v|? Justify your answer and give it a meaningful interpretation.

(a) Let vt) be a differentiable vector valued function of t. If v. (dy/dt) = 0 for all t, can we say anything about |v|?Justify your answer and give it a meaningful interpretation.

(1) Give an example of a function z = f(x, y) and a unit vector i such that f.(0,0) = 2, fy(0,0) = 1 and fã(0,0) is negative.