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

  1. #1
    Member mybrohshi5's Avatar
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    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
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  2. #2
    MHF Contributor
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    Looks fine.
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