Suppose a subspace is spanned by the set $S$ of vectors shown below.

$S = \Bigg \lbrace$$\left[\begin{array}{c}1\\7\\\end{array}\right]$, $\left[\begin{array}{c}2\\-14\\\end{array}\right]$$\Bigg \rbrace$

Find a subset of $S$ 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.

A basis for the subspace is $\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?