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).

- anonymous

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- anonymous

i think this will fail in terms of scaler multiplication

- anonymous

should have
\[a(\overline{v}+\overline{w})=a\overline{v}+a\overline{w}\]

- anonymous

but
\[a(f\oplus g)\neq af\oplus ag\]

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## More answers

- anonymous

no guarentees, but i think this is right.

- anonymous

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.

- anonymous

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.

- anonymous

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 :-)

- anonymous

yw

- anonymous

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

- anonymous

yes

- anonymous

I'm looking back at my old questions sighing at how much I do not get this stuff, lol :-)

- anonymous

Yeah it is a pain the fan's testimonial =P

- anonymous

yup

- anonymous

How long ago did you take linear algebra?

- anonymous

Mmmm like 3 years.

- anonymous

Did you solve this problem already?

- anonymous

I think I might have it written down somewhere but can't remember what the answer is right offhand

- anonymous

besides, it's Friday and I'm fighting off a head cold

- anonymous

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.

- anonymous

Satellite's answer was right. \[a(f+g)\neq af+ag\]

- anonymous

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.

- anonymous

Sorry, what does it mean "fighting off a head cold"?

- anonymous

sinus cold. I can barely form a complete thought because of it :-(

- anonymous

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

- anonymous

Sorry, I hope you'll get better.

- anonymous

You get a medal for that, lol

- anonymous

haha ty.

- anonymous

I know that one. Its good.

- anonymous

oh thank god! that give me hope of passing the second time around.

- anonymous

I wish I could recommend a book, but I learned from spanish books =P

- anonymous

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.

- anonymous

I just really suck at the notation and proofs.

- anonymous

You can see it like a videogame.

- anonymous

A game has some rules and that is all you need. So read carefully the rules(axioms) and try to understand them.

- anonymous

will do.

- anonymous

Well see you then, have a nice night.

- anonymous

I took organic chemistry a while back and we had the full solutions manual for doing our homework. I learned really well that way.

- anonymous

organic chemistry?

- anonymous

You're a genius if you know organic chemistry =P

- anonymous

Yep. I was pre-pharmacy, but changed my career goals.

- anonymous

No, it's all memory :-). You just have to do like 200 homework problems a week!

- anonymous

ohh, what are your career goals now?

- anonymous

civil engineering now. We'll see how that turns out.

- anonymous

Wooow I used to like it haha

- anonymous

what changed your mind

- anonymous

why do you not like it now?

- anonymous

I like it now

- anonymous

oh I see

- anonymous

Well my major is mechatronics, but I used to like solving structures problems.

- anonymous

Oh wow, pretty advanced

- anonymous

haha thank you, it's just a fancy name.

- anonymous

Some time ago I posted some problems like your, but no one semeed to be willing to help.

- anonymous

Yep, now I'm in that position. I don't mind helping people with stuff I remember though

- anonymous

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.

- anonymous

For instance: 15 grams of fructose in an apple vs. 15 grams fructose in some soda: which fructose is healthier?

- anonymous

Could you help me with chemistry?

- anonymous

They're the same!!!!

- anonymous

I think the apple's fructose

- anonymous

But it's the saaaaame molecule lolz

- anonymous

Ohh yeah, I'm so dumb =P

- anonymous

I didn't mean it that way :-D

- anonymous

but you get the idea

- anonymous

you have chemistry you need help with? Well I can't make any promises with helping

- anonymous

Yeah, I can't not even do an equation balance.

- anonymous

I get lost pretty soon.

- anonymous

I like those problems with finding limiting reactant. yeeeaaah

- anonymous

But I HATE redox. hate hate hate.

- anonymous

hahha me too.

- anonymous

I need some sleep. Please feel free to post LA, or Statics problems. I love them hehe

- anonymous

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

- anonymous

okay well good night

- anonymous

Hahaha thak you for bugging me then =P. Good night!

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