- #1

spaghetti3451

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## Homework Statement

Consider the ordinary vectors in three dimensions (a

_{x}, a

_{y}, a

_{z}) with complex components.

a) Does the subset of all vectors with a

_{z}= 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?

## Homework 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.

## The Attempt at a Solution

a) Yes. Dimension = 3.

b) No

c) Yes

What do you think?

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