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Math Help - Spanning sets?

  1. #1
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    Spanning sets?

    I'm confused about spanning sets...I can't find any information about them from my book and I must have forgotten going over it in class.

    Here's the question:
    "W is the subspace of R^4 consisting of all vectors of the form [a,b,a-b,a+c] where a, b, c are in R. Find a spanning set for W."

    A spanning set is a set of vectors whose linear combination is the subspace W (is this correct?)

    So would this be a spanning set?
    {a[1,0,1,1], b[0,1,-1,0], c[0,0,0,1]}
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  2. #2
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    Quote Originally Posted by paulrb View Post
    I'm confused about spanning sets...I can't find any information about them from my book and I must have forgotten going over it in class.

    Here's the question:
    "W is the subspace of R^4 consisting of all vectors of the form [a,b,a-b,a+c] where a, b, c are in R. Find a spanning set for W."

    A spanning set is a set of vectors whose linear combination is the subspace W (is this correct?)

    So would this be a spanning set?
    {a[1,0,1,1], b[0,1,-1,0], c[0,0,0,1]}
    you're almost correct! the set of three vectors \begin{bmatrix} 1 \\ 0 \\ 1 \\ 1 \end{bmatrix}, \ \begin{bmatrix} 0 \\ 1 \\ -1 \\ 0 \end{bmatrix}, \ \begin{bmatrix}0 \\ 0 \\ 0 \\ 1 \end{bmatrix} is a spanning set for W. (it's clear that these three vectors are linearly independent. so \dim W=3.)
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