Do anybody wanna remind, or no?
2 answers:
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Answer:
- The set
with x ≤ 0 and y ≤ 0 is not a vector space.
- The 10th axiom
does not hold
Step-by-step explanation:
Let u, v and w be vectors in the vector space V, and let c and d be scalars. A set S is defined as a vector space if it satisfies the following conditions:
- 1.
- 2. v + w = w + v
- 3. (u + v) + w = u + (v + w)
- 4. v + 0 = v = 0 + v
- 5. v + (−v) = 0
- 6. 1v = v
- 7. c(dv) = (cd)v
- 8. c(v + w) = cv + cw
- 9. (c + d)v = cv + dv
- 10.
Given the set of all vectors x, y in with x ≤ 0 and y ≤ 0
If the scalar c is such that .
Therefore, the 10th axiom is not satisfied and thus the set with x ≤ 0 and y ≤ 0 is not a vector space.