v1' = [2 0 -1] v2' = [0 -2 3] v3' = [1 -1 1] v4 = [1 1 -2]

mat a = (2, 0, 1, 1 \ 0, -2, -1, 1 \ -1, 3, 1, -2)
mat list a

mat b = a*a'

mat symeigen e m = b

mat list m

The following lnear combinations can be shown to exist among the v's:
v3 = (1/2)v1 + (1/2)v2
v4 = (1/2)v1 + (-1/2)*v2