Suppose that A E M2(R) is normal. (a) Prove that A is symmetric or that A...

  

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Suppose that A E M2(R) is normal. (a) Prove that A is symmetric or that A = (,) for some a, b eR with b # 0. (b) If A is normal but not symmetric, find an orthonormal eigenbasis for T LA E L(C²). %3D Suppose that A E M2(R) is normal. (a) Prove that A is symmetric or that A = (,) for some a, b eR with b # 0. (b) If A is normal but not symmetric, find an orthonormal eigenbasis for T LA E L(C²). %3D