What is the Eigenvector for a 2x2 Matrix with Eigenvalue -2?

[Ry122]

for the matrix
{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?

 

[phyzguy]

Clearly u=0, and the equations will both be satisfied for any value of v, so the normalized eigenvector is (0,1).