it just wasnt meant to be

Sunday, May 11, 2008

Theorem:
A non-void subset M of a vector space V, is a vector spaceif and only if rx + sy is in M for any r,s in R and any x,y in M.
Part 1: first we prove that If M is a vector space then rx + sy is in M for any r,s in R and any x,y in M. Well, if M is a vector space then, from the postulates, rx and sy are in M and therefore rx + sy is in M .Part 2: we prove that If rx + sy is in M for any r,s in R and any x,y in M, then M is a vector space.
Since rx + sy is in M, choose r = s = 1. So, x + y is in M
Since the associativity holds in V, it holds in M
Since rx + sy is in M, choose r = 1 s = -1. So, 0 is in M
Since rx + sy is in M, choose r = -1 s = 0. So, -x is in M
Since the commutativity holds in V, it holds in M
Since rx + sy is in M, choose s = 0. So, rx is in M
The properties of scalar multiplication hold because they hold in V.

if u actually read the theorem on top and understood, good for you. its part of vector space, its proof and its jux one portion. h3 exam is on wed and i havent finished studying. rushing through wouldnt be good cause i wouldnt understand, so im jux taking some time, while rushing past some parts which are difficult to understand. contradictory, bud yea, u get the drift. things like genetics and population growth are like - i dun understand. yes, they are part of maths, under the chapter eigenvectors and eigenvalues (LoL). lets stop talkin bout maths for now.

things in life haven exactly been any easier than it was since the beggining of the year and i dont think its gonna get any easier any time soon, especially cause swim intensive training is coming up, tgt with the sch nationals in july. im so dead in june. hope my life's turns out fine in the end.

closed under addition and scalar multiplication and containing the 0 vector...

next week wun be swimming much, cause of exams and college cleanup, hope i dont deprove cause of it. the juniors are getting faster in terms of speed, good for them i guess.

shift cipher, vigenere cipher, hill cipher, RSA, NRIC, ISBN...

college cleanup on fri and the class haven been cooperating with me. pls do, i dont wanna scream at ppl alrite. its jux bringing some stuff, it wun kill u rite. im super pissed off with some of my classmates, ripping off benefits without putting in any effort. jux pisses me off.

determinants, elementary matrices, inverses, linear combination...

as u can see im not realli in the right frame of mind for now, cya ltr peepx, after my h3 exam that is.

JoNz,
tired of it all...
5:04 PM

am i moving on...