{5,0}

{2,-2}

when determining the eigenvector for its 2nd eigenvalue, -2, you would start out by doing

{5--2 ,0}

{2 ,-2--2}

giving

{7,0}

{2,0}

In equation form this is

7u + 0v = 0

2u + 0v = 0

Ordinarily I would set u or v to a value and solve for the other letter.

But in this case this can't be done since in both equations v has a coefficient of 0.

So what would you do in this situation?