1. (a) When is the set of vectors {V₁, V₂, v} said to be linearly independent?
(b) Determine whether or not the set of vectors S = {(1, 5, -8), (1, -2, 0), (-3, 4, -5)} is a linearly independent set of vectors, and give reasons for your answer.
(c) Suppose f(t) = 5 cos 2t + 3 sin 4t. Define D²f = d/dt² (the second derivative of the function f with respect to t). Obtain the coordinates of the function D²f with respect to the basis {cos 2t, sin 4t}.