Can I choose any number for the variable when finding eigenvectors in matrices?

[sciencegirl1]

When finding eigenvectors in matrices I choose something for some x-es.

Like sometimes x3 or x4 is chosen to be s or t or 2s etc...

What I´d like to ask about is, does it not matter what the number is? Can I chose whatever I want to?

If the matrix has 3 eigenvalues and after gauss jordan I get:
100
014
000

I chose x3 to be 1.
But could I just as well chose it to be 5 or six?

 

[HallsofIvy]

When finding eigenvectors in matrices I choose something for some x-es.

Like sometimes x3 or x4 is chosen to be s or t or 2s etc...

What I´d like to ask about is, does it not matter what the number is? Can I chose whatever I want to?

If the matrix has 3 eigenvalues and after gauss jordan I get:
100
014
000

I chose x3 to be 1.
But could I just as well chose it to be 5 or six?

I have no idea what "x3 or x4" you are talking about. It is true that if you can get an eigenvector in the form <ax, bx, cx> where x is a variable you can take x to be any (non-zero) number you want. That is because any multiple of an eigenvector is also an eigenvector.