1. The problem statement, all variables and given/known data Consider the ordinary vectors in three demensions (ax, ay, az) with complex components. a) Does the subset of all vectors with az = 0 constitute a vector space? If so, what is its dimension; if not; why not? b) What about the subset of all vectors whose z component is 1? c) How about the subset of vectors whose components are all equal? 2. Relevant equations A vector space satisfies the following properties: 1. the sum of any two vectors is another vector. 2. vector addition is commutative and associative. 3. there exists a zero vector. 4. for every vector, there is an inverse vector. 5. the product of a vector with a scalar is another vector. 6. scalar multiplication is distributive w.r.t. vector addition and w.r.t. scalar addition 7. sclalar multiplication is associative w.r.t. mulitiplication of scalars. 3. The attempt at a solution a) Yes. Dimension = 3. b) No c) Yes What do you think?