The matrix

4 0 1

-2 1 0

-2 0 1

I have got the eigenvalues 1,2,3

My first question is when you do 1 first you get

3 0 1

-2 0 0

-2 0 0

So you have the equations

3U1 + U3 = 0

-2U1 = 0

- 2U1 = 0

So U1 = 0 and U3 = 0, but what does U2 equal?

Then for the eigenvalue 2 you get

2 0 1

-2 -1 0

-2 0 -1

2U1 + U3 = 0

-2U1 - U2 = 0

-2U1 -U3 =0

so U1 = 1 U2 = -2 U3 = -2 or U1 = -1 U2 = 2 and U3 = 2.My lecturer got the second answer, but it doesnt matter does it? They're both right.