i need trying to understand this using vector 6 and axiom 6:
"for your initial post you’ve been assigned one axiom from one of these candidate vector spaces to analyze. in writing your discussion board posts make sure to clearly explain and justify your work. your post should show that the axiom does or does not hold. the addition and scalar multiplication operations for all of the candidate vector spaces listed below are the "regular" addition and multiplication we always use."
for this discussion, select one of the following prompts:
five examples of vector spaces were provided without proof in the overview. in this discussion, you will verify axioms of these standard vector spaces. for your initial post, select one of the example vector spaces and verify 4 of the vector space axioms. in responding to your classmates’ posts, verify that their original work is correct, and verify an additional 2 axioms.
propose your own vector space. select 4 of the vector space axioms and verify that they do (or do not) hold. in responding to your classmates’ posts, verify that their original work is correct and show that 2 additional axioms do (or do not) hold.
candidate vector spaces
rn, the set of all dimension-n vectors for any n > = 1.
amxn, the set of all m x n matrices.
pn, the set of all polynomials of degree < = n.
c[a, b]the set of all continuous functions defined on the closed interval [a, b].
a subspace of r2: the set of all dimension-2 vectors [x; y] whose entries x and y are odd integers.
a subspace of r2: the set of all dimension -2 vectors [x; y] such that x> =0 and y> = 0. note that this is just the 1st quadrant of the 2-d plane.
a subspace of r3: the set of all dimension -3 vectors [x; y; z] such that x+y+z = 0 where x, y, and z are real-valued numbers.