Need to show that {(1,0,0)^T, (0,1,1)^T, (1,0,1)^T, (1,2,3)^T} is a spanning set for R^3.

So I use alpha, beta, gamma, and another variable to show that this entire statement can be put into a linear combination. Would I just set the last variable to be equal to 0. It seems otherwise it would be a spanning set of R^4 instead of R^3.