Prove that Zn Zn is notisomorphic to any subgroup of Zm for any m.
1 answer:
Answer and Step-by-step explanation:
Every group homomorphism ϕ:Zn→Zm extends in a unique way to a linear transformation T:Qn→Qm of vector spaces over Q.
Moreover, ϕ is injective iff T is injective. But T being injective implies n≤m.
Applying this to both ϕ and ϕ−1, we conclude that n≤m≤n.
NOTE:
The proof and step-by-step explanation is in the attachment below
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Answer:
(-2,21)
Step-by-step explanation:
2 days ago, Paulo's commute time was halfway between his commute times 8 and 9 days ago.
8 days ago means that x-coordinate -8 represents this day. Count 8 units to the left and find that when x = -8, y = 24 minutes.
9 days ago means that x-coordinate -9 represents this day. Count 9 units to the left and find that when x = -9, y = 18 minutes.
Find halfway commute time between points (-8,24) and (-9,18):
then coordinates that Paulo should graph are
(-2, 21)
(-2 means 2 days ago, 21 is the halfway)