Recent content by ksmith630

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

So I'm only working in the ring <Z,x,+> of integers?

does this sound right guys?

Ahh perfect. 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 with rationals as well as integers, would i write...

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...

Hi folks, I'm hoping to get your opinions about something. If i were given two linear equations and needed to solve for x and y using the methods of "substitution" and "elimination", what algebraic structure should i use? I can solve the systems just fine, but I'm trying to "explain" each step...

huh??

Well I know I can't do it in a group since I need two operations, and I know fractions don't exist in a ring, so what else can I pick from? I want to use the properties of real numbers in addition and mult, but to cite properties I need the algebraic structure first.

Actually we weren't given any instructions on whether to use properties from groups, rings, fields or integral domains. We must pick the structure that best represents the method of elimination and again for the method of substitution. Did I solve the systeem correctly above for each of these...

So am i in a ring of reals?

I'm guessing it shouldn't; is this an indicator that this isn't in a ring? What should i be looking for to determine this? Should indicate reals rather than integers? Maybe integral domain instead?

Thanks for the responses! So i guess i'd have to say I'm solving the system in a ring? This is what i have so far (note that i have to do this for both methods below). For the "elimination" method: x+y=5 x-y=1 1(1x+1y)=(5)1 Multiply the top equation (both sides) by 1...

Hi everyone, I'm currently taking an abstract Algebra course and need a little guidance with an analysis of solving a system of linear equations. We are given two linear equations and need to solve for x and y using the method of "substitution" and again using "elimination". However, we must...