Let A be an nn real matrix with complex eigenvalue = a + ib, where b = 0, and let v = r

Chapter 7, Problem 44

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Let A be an nn real matrix with complex eigenvalue = a + ib, where b = 0, and let v = r + is be a corresponding eigenvector of A. (a) Prove that r and s are nonzero vectors in Rn. (b) Prove that {r,s} is linearly independent in Rn. F

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