Suppose a subspace is spanned by the set of vectors shown. Find a basis for the subspace, using the method of transforming a matrix to echelon form, where the rows of the matrix represent vectors spanning the subspace.

$\Bigg \lbrace \left[\begin{array}{c}3\\5\\\end{array}\right]$, $\left[\begin{array}{c}9\\-6\\\end{array}\right] \Bigg \rbrace$

$\Bigg \lbrace$$\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$, $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$ $\Bigg \rbrace$
What is the dimension of the subspace?