# Finding subset of vectors which form a basis

Let $W = \{x \in \Bbb{R}^5 | \sum_{i=1}^5 x_i=0\}$. The following vectors span W. Find a subset of the following vectors which forms a basis for W.

$u_1 = (2, -3, 4, -5, 2)$
$u_2 = (-6, 9, -12, 15, -6)$
$u_3 = (3, -2, 7, -9, 1)$
$u_4 = (2, -8, 2, -2, 6)$
$u_5 = (-1, 1, 2, 1, -3)$
$u_6 = (0, -3, -18, 9, 12)$
$u_7 = (1, 0, -2, 3, -2)$
$u_8 = (2, -1, 1, -9, 7)$

I understand what is required to solve this problem. $Dim(\Bbb{R}^5) = 5$, so I need to throw away 3 vectors that are linearly dependent. I am wondering if there is a simple way to solve this problem, instead of checking if each vector depends on the others.

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$\dim (\mathbb{R}^5)$ may be 5, but $\dim (W)$ is only 4. –  Yoni Rozenshein Sep 26 '12 at 0:00