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Math Help - Spanning set.

  1. #1
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    Spanning set.

    A subspace of \mathbb{R}^3 is given by:
    S=\lbrace (a,b,c)|a-10b+12c=0 \rbrace

    Determine two vectors X and Y such that {X, Y} forms a spanning set for S.
    -------------------------
    Hmm...

    Now I understand that I need to find two vectors such that set of all combinations:

    \lbrace aX + bY | a, b \in R \rbrace = S
    but I'm not sure how to proceed from here...
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  2. #2
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    Quote Originally Posted by scorpion007 View Post
    A subspace of \mathbb{R}^3 is given by:
    S=\lbrace (a,b,c)|a-10b+12c=0 \rbrace

    Determine two vectors X and Y such that {X, Y} forms a spanning set for S.
    -------------------------
    Hmm...

    Now I understand that I need to find two vectors such that set of all combinations:

    \lbrace aX + bY | a, b \in R \rbrace = S
    but I'm not sure how to proceed from here...
    a- 10b+ 12c= 0 so a= 10b- 12c. Choose values for b and c and solve for a.

    I recommend, because it is easy, b= 1, c= 0 for one vector, b= 0, c= 1 for the other.
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