Answer
See below
Work Step by Step
Given $S$ be the subspace of $R^3$ consisting of all vectors of the form $v = (c_1, c_2, c_2 − c_1,c_1-2c_2)$
Rewrite $(c_1, c_2, c_2 − c_1,c_2-2c_2)=c_1(1,0,-1,1)+c_2(0,1,1,-2)$
Hence, set of vectors $(1,0,-1,1),(0,1,1,-2)$ spans $S$.
