Find the eigenvalues \lambda_1 < \lambda_2 and associated orthonormal eigenvectors of the symmetric matrix
A = \left[\begin{array}{cccc}
-1 &3 &0 &0\cr
3 &-1 &0 &0\cr
0 &0 &-1 &3\cr
0 &0 &3 &-1
\end{array}\right].

\lambda_1 =
has associated orthonormal eigenvectors \left[\Rule{0pt}{4.8em}{0pt}\right. \left]\Rule{0pt}{4.8em}{0pt}\right. , \left[\Rule{0pt}{4.8em}{0pt}\right. \left]\Rule{0pt}{4.8em}{0pt}\right. .

\lambda_2 =
has associated orthonormal eigenvectors \left[\Rule{0pt}{4.8em}{0pt}\right. \left]\Rule{0pt}{4.8em}{0pt}\right. , \left[\Rule{0pt}{4.8em}{0pt}\right. \left]\Rule{0pt}{4.8em}{0pt}\right. .

Note: The eigenvectors above form an orthonormal eigenbasis forA .

Note: The eigenvectors above form an orthonormal eigenbasis for

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