Difference between revisions of "031 Review Part 3, Problem 2"

Revision as of 13:17, 13 October 2017

Find the eigenvalues and eigenvectors of the matrix $A={\begin{bmatrix}1&1&1\\0&-1&1\\0&0&2\end{bmatrix}}.$

Foundations:
An eigenvector of a matrix $A$ is a nonzero vector ${\vec {x}}$ such that $A{\vec {x}}=\lambda {\vec {x}}$ for some scalar $\lambda .$
In this case, we say that $\lambda$ is an eigenvalue of $A.$

Solution:

Step 1:

Step 2:

Final Answer:

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 !Foundations: &nbsp;
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+|An eigenvector of a matrix &nbsp;<math style="vertical-align: 0px">A</math>&nbsp; is a nonzero vector &nbsp;<math style="vertical-align: 0px">\vec{x}</math>&nbsp; such that &nbsp;<math style="vertical-align: 0px">A\vec{x}=\lambda\vec{x}</math>&nbsp; for some scalar &nbsp;<math style="vertical-align: 0px">\lambda.</math>
+|-
+|In this case, we say that &nbsp;<math style="vertical-align: 0px">\lambda</math>&nbsp; is an eigenvalue of &nbsp;<math style="vertical-align: 0px">A.</math>
 |}