Solving for k in a Homogenous System

[HKP]

Homework Statement

Find all values of k such that the following homogenous system has non-trivial solutinos:
kx + 2y + 2z = 0
x + 2y + 2z = 0
4x + (k-1)y +2z = 0

Homework Equations

The Attempt at a Solution

I put it into matrix form ( k 2 2 0
1 2 2 0
4 (k-1) 2 0 )
Then i subtracted row 2 from row 1 to get
k 2 2 0
(1-k) 0 0 0
4 (k-1) 2 0

Then i said if k=1 then there are infinite many solutions.

I don't know where to go from that.

 

[roam]

No, that's not right at all! I think you even forgot to interchange row 2 with row 1 in order to introduce a leading 1 in a₁₁.