"suppose that y1 and y2 are linearly independent on an interval I . Prove that z1=y1+y2 and z2 = y1- y2 are also linearly independent on I." Please help proving this. I don't know where to begin. I know that linearly independent means they are set of fundamental solutions. This question appeared in the section Algebraic properties of solutions of Second-order linear differential equations. Thank you,