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## Homework Statement

Determine the eigenvalues and eigenvectors of the matric, A:

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

## Homework Equations

I think i understand what is going on. I have found the matrix equation to be:

[tex]\left(1-\lambda\right)\left[\left(-2-\lambda)(1-\lambda)-1\right]=0[/tex]

So:

[tex]\lambda_{1}=1[/tex]

[tex]\lambda_{2}=\frac{-1-\sqrt{13}}{2}[/tex]

[tex]\lambda_{3}=\frac{-1-\sqrt{13}}{2}[/tex]

## The Attempt at a Solution

I have gotten some solutions (but this being my first attempt at Tex i think would take me an age to write out!) but im confused as to which is the best method.

In lectures, our lecturer seemed to say that when you get to

[tex]V_{1}=\left[\begin{array}{ccc}x_{1}\\x_{2}\\x_{3}\end{array}[/tex]

You just set

[tex]x_{3}=1[/tex]

To make life easier and go from there. But i dont see how or why?

I always tried to use the normalisation condition that the square of the three components of the vectors equals one and find another relation from there (or sub in something else)

Could some one please help?

EDIT: Sorry for my failed attempt at Tex - only took half an hour!