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MATH 408FINAL EXAMSOLUTIONS TO SAMPLE QUESTIONSSample QuestionsQuestion1: Theory Question1. State the first- and second-order conditions for optimality for the following two problems:(a) Linear least squares: minx∈Rn12kAx-bk22, whereA∈Rm×nandb∈Rm.(b) Quadratic Optimization: minx∈Rn12xTQx+gTx, whereQ∈Rn×nis symmetric andg∈Rn.2. What is an H-orthogonal vector pair, and why must the vectors in this pair be linearly independent?