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Linear Algebra: Determine if this set is a vector space. Either show that the necessary properties are satisfied, or give an example showing that at least one of them is not. -The set P of all polynomials, with the usual definition of scalar multiplication, but with addition defined as polynomial multiplication (so f + g (morphed addition) is equal to the product of f and g).

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i think this will fail in terms of scaler multiplication
should have \[a(\overline{v}+\overline{w})=a\overline{v}+a\overline{w}\]
but \[a(f\oplus g)\neq af\oplus ag\]

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Other answers:

no guarentees, but i think this is right.
Hey thank you very much :-). I just don't get this vector space stuff at all. It's okay if it's not totally correct, I'll look for some similar examples.
actaully i am sure it is right. need to check against vector space axioms. the point of this exercise is to get you to learn them.
Yeah I understand. It's hard just trying to get a grasp on vector spaces at this point. I don't get the concept of "redefining" the axioms. It's all very strange to me. Anyway, thank you again. I will try my hardest to learn the material :-)
yw
Sorry to bug you again, but I have another question... So addition is defined as polynomial multiplication, f(+)g = f*g. Are you using (g) to show that this is not a vector space? http://tutorial.math.lamar.edu/Classes/LinAlg/VectorSpaces.aspx
yes
I'm looking back at my old questions sighing at how much I do not get this stuff, lol :-)
Yeah it is a pain the fan's testimonial =P
yup
How long ago did you take linear algebra?
Mmmm like 3 years.
Did you solve this problem already?
I think I might have it written down somewhere but can't remember what the answer is right offhand
besides, it's Friday and I'm fighting off a head cold
I think my main problem was this book we had to use. I hated it. http://www.amazon.com/Linear-Algebra-Third-John-Fraleigh/dp/0201526751 Maybe the instructors like it, but it's not student friendly.
Satellite's answer was right. \[a(f+g)\neq af+ag\]
Ohh I don't know the book. But believe me the good linear algebra books, are not friendly at all. But once you grasp the ideas you'll love the subject.
Sorry, what does it mean "fighting off a head cold"?
sinus cold. I can barely form a complete thought because of it :-(
Here's a book that I've been going through. It seems to do a better job at explaining the fundamental concepts. http://www.amazon.com/Elementary-Enhanced-WebAssign-1-Semester-Available/dp/1439044007/ref=sr_1_1?s=books&ie=UTF8&qid=1331361710&sr=1-1
Sorry, I hope you'll get better.
You get a medal for that, lol
haha ty.
I know that one. Its good.
oh thank god! that give me hope of passing the second time around.
I wish I could recommend a book, but I learned from spanish books =P
That's alright. And the other thing is, I learn through looking at tons of examples. So I'll try to get my hands on an instructors solutions manual. I don't really think it's cheating because we won't even be using that book for the class anyway.
I just really suck at the notation and proofs.
You can see it like a videogame.
A game has some rules and that is all you need. So read carefully the rules(axioms) and try to understand them.
will do.
Well see you then, have a nice night.
I took organic chemistry a while back and we had the full solutions manual for doing our homework. I learned really well that way.
organic chemistry?
You're a genius if you know organic chemistry =P
Yep. I was pre-pharmacy, but changed my career goals.
No, it's all memory :-). You just have to do like 200 homework problems a week!
ohh, what are your career goals now?
civil engineering now. We'll see how that turns out.
Wooow I used to like it haha
what changed your mind
why do you not like it now?
I like it now
oh I see
Well my major is mechatronics, but I used to like solving structures problems.
Oh wow, pretty advanced
haha thank you, it's just a fancy name.
Some time ago I posted some problems like your, but no one semeed to be willing to help.
Yep, now I'm in that position. I don't mind helping people with stuff I remember though
Even though I changed the field I'm going for, I still like ochem. After taking that class, I realized that some people can say the dumbest things.
For instance: 15 grams of fructose in an apple vs. 15 grams fructose in some soda: which fructose is healthier?
Could you help me with chemistry?
They're the same!!!!
I think the apple's fructose
But it's the saaaaame molecule lolz
Ohh yeah, I'm so dumb =P
I didn't mean it that way :-D
but you get the idea
you have chemistry you need help with? Well I can't make any promises with helping
Yeah, I can't not even do an equation balance.
I get lost pretty soon.
I like those problems with finding limiting reactant. yeeeaaah
But I HATE redox. hate hate hate.
hahha me too.
I need some sleep. Please feel free to post LA, or Statics problems. I love them hehe
I will, I'm taking statics next quarter. And yes, I will try to bug you with the hardest linalg problems I can find :-D
okay well good night
Hahaha thak you for bugging me then =P. Good night!

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