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## Homework Statement

a b c

0 b 8

0 0 c

## Homework Equations

10 axioms to determine vector space:

1. If u and v are objects in V, then u + v is in V.

2. u + v = v + u

3. u + (v + w) = (u + v) + w

4. There is an object 0 in V, called a zero vector for V, such that 0 + u = u+ 0 = for all u in V

5. For each u in V, there is an object -u in V, called a negative of u, such that u + (-u) = (-u) + u = 0.

6. If k is any scalar and u is any object in V, then ku is in V.

7. k(u + v) =ku + kv

8. (k + m)u = ku + mu

9. k(mu) = (km)(u)

10. 1u=u

## The Attempt at a Solution

I am brand new to this, but this is what I got so far.

u =

a b c

0 b 8

0 0 c

v =

a' b' c'

0 b' 8

0 0 c'

I got that it isn't a vector space because

u + v =

a + a' b + b' c + c'

0 b + b' 16 <----- Because this should be 8

0 0 c + c'

Is this correct and it would fail the 1st axiom?