Let f be a flow in a network, and let be a real number. The scalar flow product, denoted f, is a function from V

Let f be a flow in a network, and let α be a real number. The scalar flow product, denoted α f, is a function from V × V to R defined by (αf)(u, v) = α • f (u, v).
Prove that the flows in a network form a convex set. That is, show that if f1 and f2 are flows, then so is αf1 + (1 - α) f2 for all α in the range 0 ≤ α ≤ 1.