Find a basis for the subspace of $\mathbb{R}^4$ spanned by the following vectors. $$\left\lbrace \left[\begin{array}{c} 0\cr 1\cr 2\cr 0 \end{array}\right], \left[\begin{array}{c} -3\cr 1\cr -1\cr 0 \end{array}\right], \left[\begin{array}{c} -3\cr 0\cr -3\cr 0 \end{array}\right], \left[\begin{array}{c} 6\cr 0\cr 6\cr 0 \end{array}\right] \right\rbrace$$

Basis: $\Bigg\lbrace$ $\left[\Rule{0pt}{4.8em}{0pt}\right.$$\left]\Rule{0pt}{4.8em}{0pt}\right.$, $\left[\Rule{0pt}{4.8em}{0pt}\right.$$\left]\Rule{0pt}{4.8em}{0pt}\right.$ $\Bigg\rbrace.$