Difference between revisions of "031 Review Part 3, Problem 8"
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!Foundations: | !Foundations: | ||
|- | |- | ||
| − | | | + | |The eigenvalues of a diagonal matrix are the entries on the diagonal. |
|} | |} | ||
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;" | {| class="mw-collapsible mw-collapsed" style = "text-align:left;" | ||
| − | ! | + | ! |
| + | |- | ||
| + | |One example of such a matrix is | ||
|- | |- | ||
| | | | ||
| − | + | ::<math>A=\left[\begin{array}{ccc} | |
| − | + | 5 & 0 & 0\\ | |
| − | {| | + | 0 & -1 & 0\\ |
| − | + | 0 & 0 & 3 | |
| + | \end{array}\right].</math> | ||
| + | |- | ||
| + | |Since <math style="vertical-align: 0px">A</math> is a diagonal matrix, the eigenvalues of <math style="vertical-align: 0px">A</math> are the entries on the diagonal. | ||
|- | |- | ||
| − | | | + | |Hence, the eigenvalues of <math style="vertical-align: 0px">A</math> are <math style="vertical-align: -4px">5,-1,3.</math> |
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!Final Answer: | !Final Answer: | ||
|- | |- | ||
| − | | | + | | One example is <math style="vertical-align: -31px">A=\left[\begin{array}{ccc} |
| + | 5 & 0 & 0\\ | ||
| + | 0 & -1 & 0\\ | ||
| + | 0 & 0 & 3 | ||
| + | \end{array}\right].</math> | ||
|} | |} | ||
[[031_Review_Part_3|'''<u>Return to Sample Exam</u>''']] | [[031_Review_Part_3|'''<u>Return to Sample Exam</u>''']] | ||
Revision as of 19:30, 10 October 2017
Give an example of a matrix with eigenvalues 5,-1 and 3.
| Foundations: |
|---|
| The eigenvalues of a diagonal matrix are the entries on the diagonal. |
Solution:
| One example of such a matrix is |
|
|
| Since is a diagonal matrix, the eigenvalues of are the entries on the diagonal. |
| Hence, the eigenvalues of are Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 5,-1,3.} |
![{\displaystyle A=\left[{\begin{array}{ccc}5&0&0\\0&-1&0\\0&0&3\end{array}}\right].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4d8e2f505f357471fbb844c3701591980fda79a5)
| Final Answer: |
|---|
| One example is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A=\left[\begin{array}{ccc} 5 & 0 & 0\\ 0 & -1 & 0\\ 0 & 0 & 3 \end{array}\right].} |