assig11 - Math 152 Spring 2010 Assignment#11 Notes Each...

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Math 152, Spring 2010 Assignment #11 Notes: Each question is worth 5 marks. Due in class: Wednesday, April 7 for MWF sections; Tuesday, April 6 for TTh sections. Solutions will be posted Wednesday, April 7 in the afternoon. No late assignments will be accepted. 1. Find the eigenvalues and the corresponding eigenvectors of the matrix A = 1 0 0 12 7 6 - 6 - 3 - 2 . 2. It is known that A = 2 2 2 2 8 2 - 4 4 6 has eigenvalues λ 1 = 10, λ 2 = 3 + 3 i , λ 3 = 3 - 3 i . Find the corresponding eigenvectors x 1 , x 2 , and x 3 . Remember that x 3 will be the conjugate of x 2 . You can use this as a check of your work or as a short-cut. 3. Consider the matrix A = - 1 / 3 - 4 / 3 0 2 / 3 5 / 3 0 - 5 / 6 - 4 / 3 1 / 2 . (a) Verify that k 1 = ± - 1 1 - 1 ² T , k 2 = ± 0 0 1 ² T , and k 3 = ± 2 - 1 2 ² T are eigenvectors of A . Find the corresponding eigen- values λ 1 , λ 2 and λ 3 . (b) Write formulas for
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assig11 - Math 152 Spring 2010 Assignment#11 Notes Each...

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