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 2 years ago
Is this a subspace of R3?
The set of all vectors of the form <a,b,c> where a+b+c = 0
 2 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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Jemurray3
 2 years ago
Best ResponseYou've already chosen the best response.1I 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.

Jemurray3
 2 years ago
Best ResponseYou've already chosen the best response.1You 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.
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