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Homework Statement
Find the eigenvalues and eigenvectors of [tex] \left( \begin{array}{ccc} 2 & 0 & 0 \\ 0 & 3 & 4 \\ 1 & 1 & 0 \end{array} \right)[/tex]
Homework Equations
[tex]p(\lambda) = det(A - \lambda I) = 0 [/tex]
The Attempt at a Solution
[tex]A - \lambda I = \left( \begin{array}{ccc} 2-\lambda & 0 & 0 \\ 0 & 3-\lambda & 4 \\ 1 & 1 & 0 \end{array} \right)[/tex]
[tex]det(A - \lambda I) = (2 - \lambda)(-4) + 1 = 0[/tex]
[tex]-8 + 4 \lambda + 1 = 0[/tex]
[tex]4\lambda = 7[/tex]
[tex]\lambda = \frac{4}{7}[/tex]
[tex]A - \lambda I = \left( \begin{array}{ccc} \frac{1}{4} & 0 & 0 \\ 0 & \frac{5}{7} & 4 \\ 1 & 1 & 0 \end{array} \right)[/tex]
[tex]\frac{1}{4}x_1 = 0[/tex]
[tex]\frac{5}{4}x_2 + 4x_3 = 0[/tex]
Eigenvector = [tex]\left( \begin{array}{ccc} 0 \\ 0 \\ 0 \end{array} \right)[/tex]
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