# When solving a linear system for x and y, am i in a group? ring? field?

by ksmith630
Tags: field, linear, ring, solving
P: 606
 Quote by ksmith630 huh??

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

DonAntonio
P: 606
 Quote by micromass I don't see anybody claiming that your coefficients and your x,y,z need to be in the same space. I think it's an unnecessary assumption that they do. Vector spaces are precisely there for being able to solve linear systems of equations. I can solve any linear system of equation while working in a vector space. Furthermore, even if the coefficients and the x,y,z are in the same space, then I'm still working in a vector space, a one-dimensional one.

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
Math
Emeritus