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Math Help - Dimension - quick question

  1. #1
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    Dimension - quick question

    Is the dimension of a subspace in R2 1 when x=y or when x or y is zero?
    Last edited by MathSucker; March 26th 2010 at 05:50 AM.
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  2. #2
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    Like is [1,0] one dimensional or is [1,1]?
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  3. #3
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    Is the dimension of a subspace in R2 1 when x=y or when x or y is zero?
    I assume you mean x and y to represent the components of a vector is R^2. Yes, the set of vectors [x, y] with y= x, that is all vectors of the form [x, x], is a subspace of dimension 1. The set of all vectors of the form [x, 0] and the set of all vectors of the form [0, y] are also subspaces of dimension 1. In fact, the set of all vectors of the form [x, mx], for m any fixed number, is a subspace of dimension 1.

    Like is [1,0] one dimensional or is [1,1]?
    I have no idea what you mean by this. A single non-zero vector is not a subspace at all and has no "dimension". Of course, [1, 0] is in the subspace of all vectors of the form [x, 0] and [1, 1] is in the subspace of all vectors of the form [x, x].
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