Intro To Geom Ongoing BC

Question 1

Axioms?

Answer 1

For all a,b in V 
a+b = b+a
(a+b)+c=a+(b+c)
There exists 0: 0 + a = a + 0 = a 
For all, there exist (-a) such that a+ (-a) =0
λ(a+b) = λa + λb
(λ + μ)a = λa + μb 
1a = a

Question 2

Affine space

Answer 2

With associated vector space V is a space A (of periods) with the full…?

Question 3

Dimension

Answer 3

Vector space V has a dimension n if there exists n linearly independent vectors and every n+1 vectors are linearly dependent

Question 4

Linearly independent

Answer 4

A set of vectors {x_1….x_k} is linearly independent of there does not exist non trivial linear combination of these vectors which vanishes, Σλx =0.

Question 5

Basis

Answer 5

Let V be n dimensional vector space, an ordered set {e1 … en} of linearly independent of vectors is called a basis.