# hw5 - Problems 5.1 5.2 and 5.6 from Axler Problem B The...

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Winter 2011 Math 67 Linear Algebra Homework 5 Problem A. Using the row reduction method, determine the set of solutions of the system of equation Ax = b where ( a ) A = 1 1 1 - 1 0 2 , b = 2 0 2 ( b ) A = 1 10 - 2 5 - 3 4 2 1 0 , b = 20 8 6 ( c ) A = 1 1 1 - 1 0 2 , b = 2 0 3 ( d ) A = 1 10 - 2 1 5 - 3 4 1 2 1 0 1 , b = 20 8 6 Remember, as you do the row reduction (no changing the columns!), your goal have a matrix that looks like 0 0 1 * * 0 0 * ... * 1 0 * ... * 1 * ... * . . . If you are strugling, do (b) and (d) ﬁrst and then try the other two.

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Unformatted text preview: Problems 5.1, 5.2 and 5.6 from Axler. Problem B. The eigenvalues of the linear map T : C 3 → C 3 associated to the matrix 1 1 0 1 0 1 0 1 1 are 1,-1, and 2. Determine the corresponding eigenvectors. Problem C. The eigenvalues of the linear map R : C 2 → C 2 given by the matrix ± 1-1 1 1 ² 1 2 are 1 + i and 1-i , where i = + √-1 = e πi/ 2 . Determine the corresponding eigenvectors....
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hw5 - Problems 5.1 5.2 and 5.6 from Axler Problem B The...

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