Solving Linear Systems with Hermitian Matrices

[tamtam402]

Homework Statement

I can find my eigenvalues just fine, and they're both real, as expected. My first eigenvalue is -3, which I know is correct.

I have the equations 5x+(3-i)y=0, (3+i)x+2y=0

Both of the equations come from my hermitian matrix, after I substituted λ=-3.

Homework Equations

The Attempt at a Solution

I have absolutely no idea how to solve this. This case is simple enough to be solved by trial and error, but how would I proceed if I had harder equations?

I can't use both equations since I get x=x or y=y if I substitute one into the other, since they're both the same equation.

 

[tamtam402]

Nevermind, doing another (easier) exercise allowed me to see that I only have to set ax = by, and force a value to either x or y.