- #1
SNOOTCHIEBOOCHEE
- 145
- 0
Homework Statement
let a,b [tex]\in[/tex]G show that ax=b has a unique solution in G
The Attempt at a Solution
i know what needs to be done, i just don't know how to do it.
Want to prove:
1. There is a solution
2. solution is unique
to prove uniquness of a soltuion just suppose you have a different solution x' and show that x'=x
to show that there is a solution (im not sure this part is right, cause it seems too simple) simply multiply (left) by [tex]a^{-1}[/tex]
that is [tex]a^{-1}[/tex]*ax=[tex]a^{-1}[/tex]b
we can do this because a is in the group, which implies [tex]a^{-1}[/tex] is in the group
THis is where i am stuck... i really don't know how to proceed. Have i even done the first part right?
any help appreciated