# Math Help - Basis of S - can someone please check my work

1. ## Basis of S - can someone please check my work

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

2. Looks fine.