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Math Help - Basis for a subspace and dimension

  1. #1
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    Question Basis for a subspace and dimension

    Find a basis for the subspace W of R^5 given by...


    W = {x E R^5 : x . a = x . b = x . c = 0}, where a = (1, 0, 2, -1, -1), b = (2, 1, 1, 1, 0) and c = (4, 3, -1, 5, 2).


    Determine the dimension of W. (as usual, "x . a" denotes the dot (inner) product of the vecotrs x and a).

    Please show working, your help is much appreciated.
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  2. #2
    MHF Contributor

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    Re: Basis for a subspace and dimension

    can you solve the system of equations:

    x1 + 2x3 - x4 - x5 = 0
    2x1 + x2 + x3 + x4 = 0
    4x1 + 3x2 - x3 + 5x4 + 2x5 = 0

    that's 3 equations in 5 unknowns. assuming the equations are independent (are your 3 vectors linearly independent?), how many "free variables" will you have? how does this help you choose a basis for W?
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