Let F be the vector space of infinitely differentiable functions from R to R. Consider the subspace: W = span{e^t, sin(2t), cos(3t)} 1. Show that the three vectors above are linearly independent. Consider the linear operator T: W->W d? T(f) = f"(t) – af(t) = 2 - al) For which real values of a is T invertible 2.

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