Are these vectors spanning sets

Is the following set of vectors in R^3 a spanning set for R^3 ??

{ (-1, 1, 1), (-1, 2, 1), (-5, 8, 5), (3, -1, 3) }

How do we figure this out?

A set S = {v1, v2, v3, v4} of vectors in R^3 spans R^3 if

c1v1 + c2v2 + c3v3 + c4v4 = d1w1 + d2w2 + d3w3

where v1,v2,v3 and v4 are the given vectors and

w1=(1,0,0),w2=(0,1,0) and w3=(0,0,1)

Solve the matrix equation by reducing it to the reduced row echelon form

[-1 -1 -5 3]...[1 0 0]
[1 2 8 -1]=...[0 1 0]
[1 1 5 3]......[0 0 1]

Using row operations you get

[1 0 2 0]........[-7/6 -1 5/6]
[0 1 3 0]=......[2/3 1 -1/3]
[0 0 0 1]........[1/6 0 1/6]

This means that

c1+ 2c3=-7/6 d1-d2+5/6 d3

c2+c3=2/3 d1 +d2- 1/3 d3

c4=1/6 d1+ 1/6 d3

This system is consistent which means that the given set of vectors spans R^3