does (0,0,0,0) span {( 2,1,0,3), (3,-1,5,2), ( -1, 0 2,1)}

i tried to use Gaussian elimination and i found that the the coefficients for these 3 vectors to be expressed as a combination of the zero vector have to be all 0.

this should mean that there exist no linear combi of these 3 vectors that will give the zero vector and hence the zero vector does not span {( 2,1,0,3), (3,-1,5,2), ( -1, 0 2,1)} right?

but my answer states that it spans {( 2,1,0,3), (3,-1,5,2), ( -1, 0 2,1)}....

did i do sth wrongly?