## Elementary Linear Algebra 7th Edition

A basis for the subspace is given by $$\{1,2,2),(0,0,1)\}.$$
Let $S$ be given by $$S=\{(1,2,2),(-1,0,0),(1,1,1)\}$$ We form the matrix $$\left[ \begin {array}{ccccc} 1&2&2\\ -1&0&0\\ 1&1&1 \end {array} \right].$$ The reduced form of the matrix is given by $$\left[ \begin {array}{ccc} 1&1&2\\ 0&1&2 \\ 0&0&1\end {array} \right] .$$ A basis for the subspace is given by $$\{1,2,2),(0,0,1)\}.$$