Question 893904
{{{2x+2y+z=0}}}
{{{3x+3y-2z=0}}}
{{{x+y-3z=0}}}
Use row operations to show that rows 1 and 3 and rows 2 and 3 lead to {{{z=0}}}. 
{{{R[1]-2R[2]=0}}}
{{{R[2]-3R[3]=0}}}
That leaves you with 
{{{x+y=0}}}
{{{y=-x}}}
So only 1 independent choice of variables. 
{{{dim(W)=1}}}