Find the eigenvalues \lambda_1 < \lambda_2 and associated unit eigenvectors \vec{u}_1, \vec{u}_2 of the symmetric matrix
A = \left[\begin{array}{cc}
-4 &2\cr
2 &-1
\end{array}\right].

The smaller eigenvalue\lambda_1 =
has associated unit eigenvector \vec{u}_1 = \left[\Rule{0pt}{2.4em}{0pt}\right. \left]\Rule{0pt}{2.4em}{0pt}\right. .

The larger eigenvalue\lambda_2 =
has associated unit eigenvector \vec{u}_2 = \left[\Rule{0pt}{2.4em}{0pt}\right. \left]\Rule{0pt}{2.4em}{0pt}\right. .

Note: The eigenvectors above form an orthonormal eigenbasis forA .

The smaller eigenvalue

The larger eigenvalue

Note: The eigenvectors above form an orthonormal eigenbasis for

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