Question: Problem 1 Are the following statements true or false? If true, write a proof; If false, give a counter-example. (a) Let A, BE Rox be

Problem 1 Are the following statements true or false? If true, write a proof; If false, give a counter-example. (a) Let A, BE Rox" be two symmetric matrices such that AB = BA. Then, there exist an orthog- onal matrix P and two diagonal matrices D, D', such that A = PDP? and B = PD'PT. (b) Consider linear equation Ar = b for matrix A c Rox" and vectors x, b E R". Then, the Gauss-Seidel iteration algorithm always converges to a true solution a*

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