1. Suppose that u <?xml:namespace prefix = v ns = \"urn:schemas-microsoft-com:vm

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1. Suppose that u<?xml:namespace prefix = v ns = "urn:schemas-microsoft-com:vml" /> <?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />and vare two eigenvectors of a matrix A corresponding to the same eigenvalue lambda. Show that any linear combination of u and v(assuming it is not equal to 0) is also an eigenvector of A with the same eigenvalue.

2.Suppose that vis an eigenvector of A corresponding to eigenvalue lambda. Explain why vis also an eigenvector of A^k for a positive integer k. What is its eigenvalue?

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