Question

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

Answer 1

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.

Answer 2

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.

Answer 3

Thank you!