2. Vector Spaces

Question 1

what are the 8 axioms of vector spaces

Answer 1

1. x+(y+Z) = (X+Y)+Z
2. X+Y = Y+X
3. There exists 0 such that 0+x=x
4. or all x c X there exists -x such that x+x= 0
5. L(X+Y) = LX+LY
6. (L+U)X = LX + UX
7. L(UX) = (LU)X
8. 1 * x = x

Question 2

what is a vector space

Answer 2

Set X with operations of Addition X x X -> X and scalar multiplication F x X -> F

Question 3

When is a subset a subspace

Answer 3

1) it is non-empty usually containing the identity element
2) x + y c X for all x,ycX
3) Lx c X for all LcF