Basis of S - can someone please check my work

**mybrohshi5** · March 30th 2010, 08:25 AM

Let S = $\begin{bmatrix}2\\1\\0\\4 \end{bmatrix} \begin{bmatrix}1\\3\\4\\-4 \end{bmatrix} \begin{bmatrix}3\\4\\4\\0 \end{bmatrix}\begin{bmatrix}4\\-3\\-3\\-2 \end{bmatrix}$

and let W be the subspace spanned by S.

Find a basis for W and the dimension of W.

I found the vectors

$\begin{bmatrix}2\\1\\0\\4 \end{bmatrix} \begin{bmatrix}1\\3\\4\\-4 \end{bmatrix} \begin{bmatrix}4\\-3\\-3\\-2 \end{bmatrix}$

to be Linearly Independent so the basis of W would just be these

$\begin{bmatrix}2\\1\\0\\4 \end{bmatrix} \begin{bmatrix}1\\3\\4\\-4 \end{bmatrix} \begin{bmatrix}4\\-3\\-3\\-2 \end{bmatrix}$

and the dimension of W would then be 3.

Does that all look right?

Thanks for checking

**dwsmith** · April 24th 2010, 05:21 PM

Looks fine.

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