In the last 2 weeks we've begun learning about eigenvalues/vectors. It will come up in my exam in January so I'm trying hard to get my head around this. I've tried various different sources to learn this but I'm hoping someone here can offer a different view on it. Basically, I can work out the eigenvalues no problem but that's as far as I can get.(adsbygoogle = window.adsbygoogle || []).push({});

basic example:

[tex]A= \begin{bmatrix}2 & 0 \\ 0 &-1\end{bmatrix}[/tex]

Using det(λI-A) I get that the eigenvalues are λ = 2 and λ = -1.

Then: [tex]\begin{bmatrix}2 & 0 \\ 0 &-1\end{bmatrix} \begin{bmatrix}x_{1}\\x_{2}\end{bmatrix} = \lambda \begin{bmatrix}x_{1}\\x_{2}\end{bmatrix}[/tex]

After this I'm not sure how to solve it or how to write it. I thought I had to start with λ = 2 and substitute it into the equation above, giving: [tex]2x_{1} + 0x_{2} = 2x_{1}[/tex][tex]0x_{1} - 1x_{2} = 2x_{2}[/tex] but from here I really don't know what to do. Can someone please tell me if I'm along the right tracks and explain simply what to do next?

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# Homework Help: Eigenvectors - stuck on the basics

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