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When solving a linear system for x and y, am i in a group? ring? field? 
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#19
May412, 06:21 PM

P: 606

If you don't quote it is impossible to know whom you're addressing. DonAntonio 


#20
May412, 06:28 PM

P: 606

From the example the OP presented I think it was clear that he/she was struggling with the idea that of what alg. structure her/his equations' coefficients were to be taken from, and thus what operations and elements could be used. This isn't answered by working with vector spaces as one can't multiply vectors in general vector spaces. Vectors spaces provide, among other things, an adequate alg. frame in which we can work with linear equations, but the basic operations with vectors usually have a field (or division ring) as base alg. structure from where the operations are taken. This is what I meant. DonAntonio 


#21
May412, 08:15 PM

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#22
May412, 10:04 PM

P: 10

Ohh OK i see now. I'll choose the field then but how do i write the notation? I know if i was working in a group i'd write:
"To solve, i will be in the group <Z,+> where + is the ordinary binary operation in Z." So for this system in the field, would i write: "To solve, i will be in the field <Q,+,x> where + and x are the ordinary binary operations in Q." ? 


#23
May712, 02:27 PM

P: 10

does this sound right guys?



#24
May712, 03:17 PM

P: 10

or what about if i worked in the ring of rationals?



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