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Find the eigenvalues and eigenvectors for $A = \left[\begin{array}{cc} 3 &10\cr -5 &13 \end{array}\right]$ .

The eigenvalue $a + b i =$ has an eigenvector $\left[\Rule{0pt}{2.4em}{0pt}\right.$ $\left]\Rule{0pt}{2.4em}{0pt}\right.$ .

The eigenvalue $a - b i =$ has an eigenvector $\left[\Rule{0pt}{2.4em}{0pt}\right.$ $\left]\Rule{0pt}{2.4em}{0pt}\right.$ .

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