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Unformatted text preview: 4 1 − 2 A = 16 − 2 − 8 ⎞ ⎝ 4 ⎠ − 2 − 2 determine the eigenvalues. (2 pts) c. Use the results from part b to explain why A is not invertible. (2 pts) 5. Let X, Y be n × n matrices such that X 3 = Y 3 and X 2 Y = Y 2 X . What are necessary and suﬃcient conditions on X and Y such that X 2 + Y 2 is invertible? (4 pts) ± 1 MIT OpenCourseWare http://ocw.mit.edu 18.024 Multivariable Calculus with Theory Spring 2011 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
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 Spring '11
 ChristineBreiner
 Linear Algebra, Multivariable Calculus, pts

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