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goodz

  • 3 years ago

Is this a subspace of R3? The set of all vectors of the form <a,b,c> where a+b+c = 0

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  1. Jemurray3
    • 3 years ago
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    I think you misunderstood the question. a, b, and c are components of the vector, not vectors themselves. This set of vectors forms a plane through the origin, and therefore constitutes a subspace.

  2. Jemurray3
    • 3 years ago
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    You can easily check the requirements for a subspace, also -- i.e. multiply any such vector by a scalar and its components will still add to zero, and the sum of any two such vectors is another vector whose components add to zero.

  3. goodz
    • 3 years ago
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    Thank you!

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