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Math Help - Eigen Space

  1. #1
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    [Solved] Eigen Space

    \begin{bmatrix}<br />
3 & 2\\ <br />
4 & 1<br />
\end{bmatrix}
    det(A-\lambda I)=\begin{vmatrix}<br />
3-\lambda & 2\\ <br />
4 & 1-\lambda<br />
\end{vmatrix}=(3-\lambda)(1-\lambda)-8=\lambda^2-4\lambda-5
    \lambda_{1}=5 and \lambda_{2}=-1
    When \lambda=5, \begin{bmatrix}<br />
-2 & 2\\ <br />
4 & -4<br />
\end{bmatrix}\Rightarrow \begin{bmatrix}<br />
1 & -1\\ <br />
0 & 0<br />
\end{bmatrix}
    The eigenspace for \lambda_{1} is \begin{bmatrix}<br />
1\\ <br />
1<br />
\end{bmatrix}
    When \lambda=-1, \begin{bmatrix}<br />
4 & 2\\ <br />
4 & 2<br />
\end{bmatrix}\Rightarrow \begin{bmatrix}<br />
1 & \frac{1}{2}\\ <br />
0 & 0<br />
\end{bmatrix}
    The eigenspace for \lambda_{2} is \begin{bmatrix}<br />
1\\ <br />
-2<br />
\end{bmatrix}

    Solved nevermind
    Last edited by dwsmith; April 14th 2010 at 05:36 PM.
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