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# hw6 - Determine the eigenvectors of A = 1 2 3 4 3 4 3 3 2 1...

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Winter 2011 Math 67 Linear Algebra Homework 6 Problems 5.9, 5.14 and 5.19 from Axler. Problem A. Consider the matrices P = ± 0 1 0 0 ² Q = ± 0 0 1 0 ² Compute PQ and QP . Problem B. Consider the matrix P = ± 1 - 1 1 1 ² Verﬁy that P 2 - 2 P +2 I is the zero matrix. Use this to guess what the eigenval- ues might be and prove you are correct by ﬁnding corresponding eigenvectors. Problem C. Determine a basis of C 4 consisting of eigenvectors of 1 2 4 7 3 5 8 6 9 10
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Unformatted text preview: . Determine the eigenvectors of A = 1 2 3 4 3 4 3 3 2 1 Do you have a basis of C 4 ? Explain why this must be so. Problem D. Consider the second matrix A that occured in the previous problem. Compute the two matrices ( A-3 · I ) 2 and ( A-1 · I ) 2 and determine their respective nullspaces. (Hint: Each nullspace is 2-dimensional, right?) 1...
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