Understanding the Proof of Solution Sets in Linear Systems

[miglo]

so I've been reading jim hefferon's linear algebra book
i don't know if anyone on the forum has seen it, but I am only on the first chapter and I am stuck with a proof
the proof is about the solution sets of linear systems, basically how a general solution can be described as a particular solution + a homogenous solution, that right there i understand(at least i think i understand it) but when he goes on to the proof i get lost, this is not homework or anything that was assigned to me, just some self studying I am doing on linear algebra and would really like to understand the proof

heres the link to the book
http://joshua.smcvt.edu/linearalgebra/ the proof starts on page 20 and he breaks it up into two parts

if anyone could please check it out and help me understand the proof, it would be greatly appreciated

thanks in advance!

 

[lj19]

Is this the proof?
http://en.wikibooks.org/wiki/Linear_Algebra/General_=_Particular_+_Homogeneous

 

[miglo]

yeah, didnt know it was on wikibooks

can you help me out?

 

[lj19]

I'm sorry, this is a much higher level of math than I can understand. But I thought I could help by finding that page for you.

 

[miglo]

ohh i see, its ok
ive only gone up to calculus ab in high school, and well i was never introduced to any sort of proofs during calculus ab, maybe i should learn calculus bc or calculus 2, and multivariable calculus first, then start linear algebra
the reason why i decided to learn linear algebra was because it looked really interesting to me, but I am not sure if it requires calculus 1-3 as a prerequisite to fully understand it