Difference between revisions of "031 Review Part 3, Problem 6"
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| − | <span class="exam"> | + | <span class="exam"> (a) Show that if <math style="vertical-align: 0px">\vec{x}</math> is an eigenvector of the matrix <math style="vertical-align: 0px">A</math> corresponding to the eigenvalue 2, then <math style="vertical-align: 0px">\vec{x}</math> is an eigenvector of <math style="vertical-align: -2px">A^3-A^2+I.</math> What is the corresponding eigenvalue? |
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| − | + | <span class="exam">(b) Show that if <math style="vertical-align: -3px">\vec{y}</math> is an eigenvector of the matrix <math style="vertical-align: 0px">A</math> corresponding to the eigenvalue 3 and <math style="vertical-align: 0px">A</math> is invertible, then <math style="vertical-align: -3px">\vec{y}</math> is an eigenvector of <math style="vertical-align: 0px">A^{-1}.</math> What is the corresponding eigenvalue? | |
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Revision as of 19:25, 9 October 2017
(a) Show that if is an eigenvector of the matrix corresponding to the eigenvalue 2, then is an eigenvector of What is the corresponding eigenvalue?
(b) Show that if is an eigenvector of the matrix corresponding to the eigenvalue 3 and is invertible, then is an eigenvector of What is the corresponding eigenvalue?
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Solution:
(a)
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(b)
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| (a) |
| (b) |