- #1
kq6up
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Homework Statement
Find the eigenvectors of: ##
\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr}
5 & 0 & \sqrt{3} \\
0 & 3 & 0 \\
\sqrt{3} & 0 & 3
\end{array}\right)
##
Homework Equations
##(\mathbf{A}-\lambda\mathbf{I})\cdot\mathbf{x}=0##
The Attempt at a Solution
I get the correct eigenvectors for ##\lambda=2,6##, but I don't understand why the eigenvector is ##\hat{j}## when ##\lambda=3##.
When ##\lambda=3##, the matrix becomes ##
\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr}
2 & 0 & \sqrt{3} \\
0 & 0 & 0 \\
\sqrt{3} & 0 & 0
\end{array}\right)
##. The first row yields a function ##2x-\sqrt{3}z=0##. The points that satisfy this equation do not lay along ##\hat{j}##. What am I missing?
Thanks,
Chris