The complex functions z(t), t ∈ R, can be differentiated a number of times and are a vector space V :
W = span(e-t, e-it, et, eit) and W is a subspace of V.
Which of the following 3 functions belong to W ?
z1(t) = 3et, z2(t) = cos(t), z3(t) = sinh(t)
If the functions were vectors for example like this W= span((1,2),(2,1)) and I had to determine if the vector (-2,3) belonged to W, I would solve the inhomogeneous linear system but since it's not I have no idea how to determine this.
I hope that somebody can give me a hint.
Sorry for the bad description.