Chapter 1

Question 1

Definition of a vector space

Answer 1

A vector space is a set V equipped with the following data.

1. Addition operation
2. A zero vector
3. Scalar multiplication operation.

And it should satisfy the 8 rules

Question 2

What do we need to do to prove a certain set can be give the structure of a vector space?

Answer 2

1. Define a set V
2. Define the data of an addition operation, a zero vector and a scalar multiplication operation
3. Then this data should satisfy the 8 rules

Question 3

Definition of a Subspace

Answer 3

A subset U of a vector space V is called a subspace iff

For all u, u’EU, u + u’ E U
Zero vector is element of U
for all scalars k and all vectors u element of U, k*u is an element of U