Question

i saw this question asked here and it was from 3 years ago with no answer. does anyone have any advice or suggestions for this question

show that R^(mxn) together with the usual addition and scalar multiplication of matrices satisfies the eight axioms of a vector space

Answer 1

Well, do you know what the eight axioms of a vector space are?

Answer 2

yes. they are in my book in front of me. i dodnt type them though. if you need me to i can

Answer 3

didnt*

Answer 4

OK, do you know how to do proofs of them?

Answer 5

not really. the only pre-req for linear algebra was cal 1 but most people in my class have already had discrete math or some other proof based math class.

Answer 6

he uses symbols and abbreviations i have to ask whatthey mean or google them after class

Answer 7

Basically, the proofs will be to show it with steps in algabraic form where your variables are any valid value. If they can work, then you have proven how it works.

Answer 8

These have some short explanations and examples:

http://www.math.columbia.edu/~thaddeus/linear/proof.pdf
http://www.math.ucdenver.edu/~esulliva/LinearAlgebra/Proofs.pdf

There are lots of other references, but those are pretty to the point...

Answer 9

alright thanks. i also just started googling and think i found some stuff similiar to what you just posted. i, going to look at them now

Answer 10

kk. If you get stuck, ask again. It has been a bit since I did any LA Proofs, but I may be able to work through with you. And we have some math majors around that may have even more info.

Answer 11

alright. it might be awhile before i get back though but if i get stuck ill be back

Answer 12

@e.mccormick . just letting you know i figured it out. took a while, some reading and youtube videos but it wasnt that hard once i started understanding the 8 axioms and how to apply them to matrices abstractly..

Answer 13

Ah, good. The abstract part is reayy what proofs are about. There is also a free book on proofs if you want... and some other topics:
http://aimath.org/textbooks/approved-textbooks/

To be in that list they MUST be used at a school other than the author's and survive peer review, so these are all activly used textbooks. Now, that does not mean all of them are easy to read... but the price is right for giving them a look.