How to show that $e^{a_0t},\dots,e^{a_nt}$ form a Chebyshev system on any interval? I have a hint saying that I should use Rolle's theorem, but I don't see how Rolle's theorem can give an upper bound on the number of zeroes.
A system of real functions $\{u_k(t)\}^n_{k=0}$ is a Chebyshev system if any linear combination of the $u_i$'s has at most $n$ zeroes.
