Suppose a subspace is spanned by the set $S$ of vectors shown. Find a subset of $\mathbf S$ that forms a basis for the subspace, using the method of transforming a matrix to echelon form, where the columns of the matrix represent vectors spanning the subspace.

$S = \Bigg \lbrace$$\left[\begin{array}{c}1\\-2\\-5\\-3\\\end{array}\right]$, $\left[\begin{array}{c}4\\-7\\-22\\-13\\\end{array}\right]$, $\left[\begin{array}{c}0\\9\\-18\\-9\\\end{array}\right]$$\Bigg \rbrace$

A basis is $\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$

What is the dimension of the subspace?