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
- 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.
Answer:
2 solutions x = 3 y = -2.
Step-by-step explanation:
x + 2y = –1
2x + 3y = 0
Multiply first equation by -2:
-2x - 4y = 2 Adding this to second equation:
- y = 2
y = -2.
Plug this into first equation:
x - 4 = -1
x = 3.