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Set of fundamental solutions

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"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.

Reference no: EM132077977

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