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## Homework Statement:

- Confusion in finding eigenvector? (example shown below)

## Relevant Equations:

- matrix multiplication

upon finding the eigenvalues and setting up the equations for eigenvectors, I set up the following equations.

So I took b as a free variable to solve the equation int he following way.

But I also realized that it would be possible to take a as a free variable, so I tried taking a as a free variable too.

But now I am confused because this results in vectors that is different in sign. Can anyone explain whether I should use a or b as a free variable?

So I took b as a free variable to solve the equation int he following way.

But I also realized that it would be possible to take a as a free variable, so I tried taking a as a free variable too.

But now I am confused because this results in vectors that is different in sign. Can anyone explain whether I should use a or b as a free variable?