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## Homework Statement

For a few problems dealing with eigenvectors, I substituted my eigenvalues into the characteristic equations. I got systems of linear equations. I need to find the general solution to the systems in order to find the corresponding eigenvectors.

For example in one problem I have to solve:

[tex]A = \left[\begin{array}{ccccc} -3&-3 \\ -4&-4 \end{array}\right][/tex] [tex]\left[\begin{array}{ccccc} x\\ y \end{array}\right][/tex] [tex]= \left[\begin{array}{ccccc} 0\\ 0 \end{array}\right][/tex]

-3x-3y=0

-4x-4y=0

It looks as if x,y are equal. I think I might need to write one in terms of the other but I'm no sure which.

or for example the system of equations:

-x-y-z=0

-x-y-z=0

-x-y-z=0

We have 3 variables and 3 equations which are exactly the same. How do we decide which variable to use as the "free" variable?

Thanks.