Eigen Space

**dwsmith** · April 14th 2010, 03:33 PM

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

Solved nevermind

**HallsofIvy** · April 15th 2010, 06:10 AM

Thread: Eigen Space

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