Consider the space of all functions of the form a + bt + cet + de-t, where a, b, c, d are scalars. (a) What function in the space corresponds to the sum of (1, 2, 3, 4) and (- 1, - 2, 0, - 1), assuming that we represent a function in this space as the vector (a, b, c, d)?
(b) Is cosh(t) in this space? That is, does cosh(t) correspond to some choice of a, b, c, d?
(c) What matrix corresponds to differentiation of functions on this space?