Hello, I am trying to get to grips with eigenvectors and seem to do ok until I get to one question, so I am wondering if perhaps the lecturer has given the wrong answer. The matrix is:

5 0 6

0 11 6

6 6 -2

And the eigenvalues are 14, 7 and -7. The lecturer gets the following eigenvectors:

14

2

6

3

7

6

-3

2

-73

2

-6

I can't seem to get these, mainly the y values. For example, I will do for lambda=14

-9 0 61)-9x +6z=0

0 -3 62)-3y+6z=0

6 6 -163)6x+6y-16z=0

1)6z=9x (2z=3x)

2)6z=3y (2z=y)

So I think that should be

3

1

2

I'm sure my problem lies with how I arrange the numbers in the eigenvector answer, but I just don't know, it always seems to be the part I get wrong. Would someone mind explaining how to do it properly? Thanks in advance, I have been banging my head against this for days now and will be very thankful if someone can enlighten me!