ok, let me see if i have got this right, take the same matrix again but this time with an eigenvalue of 4
so you get [3x,5x+4y,3x+6y+z] again but this time it has to equal to 4
3x = 4x
5x+4y = 4y
3x+6y+z = 4z
so the first gives x=1.3 the second gives y=0 and the third gives z=1.3...