# Finding the basis for a subspace given the span of a set of vectors

Let U = span{$u_1, u_2, u_3$},

where

$u_1 = \begin{pmatrix} 1 \\ 2 \\ 1 \end{pmatrix}$, $u_2 = \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix}$, $u_3 = \begin{pmatrix} 2 \\ 2 \\ 2 \end{pmatrix}$,

We are to find a basis {$w_1, w_2, w_3$} for U.

The first step that I have been taught to do this, is to have a matrix C with $u_1, u_2, u_3$ as rows. Why put them into rows?

(Did a brief check on similar questions, none of them answer my question. A brief Google search does bring up similar questions, but none of them answer why we put the {$u_1, u_2, u_3$} into rows.

• Thanks for your comment. I'm well aware of row reducing the matrix. I'm just wondering why we put that into rows, and not row reduce the matrix with ${u_1, u_2, u_3}$ as columns instead. – MathsWanderer Sep 3 '15 at 21:28