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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).
 2 years ago
 2 years ago
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).
 2 years ago
 2 years ago

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satellite73Best ResponseYou've already chosen the best response.3
i think this will fail in terms of scaler multiplication
 2 years ago

satellite73Best ResponseYou've already chosen the best response.3
should have \[a(\overline{v}+\overline{w})=a\overline{v}+a\overline{w}\]
 2 years ago

satellite73Best ResponseYou've already chosen the best response.3
but \[a(f\oplus g)\neq af\oplus ag\]
 2 years ago

satellite73Best ResponseYou've already chosen the best response.3
no guarentees, but i think this is right.
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
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.
 2 years ago

satellite73Best ResponseYou've already chosen the best response.3
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.
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
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 :)
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
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
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
I'm looking back at my old questions sighing at how much I do not get this stuff, lol :)
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
Yeah it is a pain the fan's testimonial =P
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
How long ago did you take linear algebra?
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
Did you solve this problem already?
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
I think I might have it written down somewhere but can't remember what the answer is right offhand
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
besides, it's Friday and I'm fighting off a head cold
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
I think my main problem was this book we had to use. I hated it. http://www.amazon.com/LinearAlgebraThirdJohnFraleigh/dp/0201526751 Maybe the instructors like it, but it's not student friendly.
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
Satellite's answer was right. \[a(f+g)\neq af+ag\]
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
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.
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
Sorry, what does it mean "fighting off a head cold"?
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
sinus cold. I can barely form a complete thought because of it :(
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
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/ElementaryEnhancedWebAssign1SemesterAvailable/dp/1439044007/ref=sr_1_1?s=books&ie=UTF8&qid=1331361710&sr=11
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
Sorry, I hope you'll get better.
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
You get a medal for that, lol
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
I know that one. Its good.
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
oh thank god! that give me hope of passing the second time around.
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
I wish I could recommend a book, but I learned from spanish books =P
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
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.
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
I just really suck at the notation and proofs.
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
You can see it like a videogame.
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
A game has some rules and that is all you need. So read carefully the rules(axioms) and try to understand them.
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
Well see you then, have a nice night.
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
I took organic chemistry a while back and we had the full solutions manual for doing our homework. I learned really well that way.
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
You're a genius if you know organic chemistry =P
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
Yep. I was prepharmacy, but changed my career goals.
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
No, it's all memory :). You just have to do like 200 homework problems a week!
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
ohh, what are your career goals now?
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
civil engineering now. We'll see how that turns out.
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
Wooow I used to like it haha
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
what changed your mind
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
why do you not like it now?
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
Well my major is mechatronics, but I used to like solving structures problems.
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
Oh wow, pretty advanced
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
haha thank you, it's just a fancy name.
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
Some time ago I posted some problems like your, but no one semeed to be willing to help.
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
Yep, now I'm in that position. I don't mind helping people with stuff I remember though
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
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.
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
For instance: 15 grams of fructose in an apple vs. 15 grams fructose in some soda: which fructose is healthier?
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
Could you help me with chemistry?
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
They're the same!!!!
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
I think the apple's fructose
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
But it's the saaaaame molecule lolz
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
Ohh yeah, I'm so dumb =P
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
I didn't mean it that way :D
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
but you get the idea
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
you have chemistry you need help with? Well I can't make any promises with helping
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
Yeah, I can't not even do an equation balance.
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
I get lost pretty soon.
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
I like those problems with finding limiting reactant. yeeeaaah
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
But I HATE redox. hate hate hate.
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
I need some sleep. Please feel free to post LA, or Statics problems. I love them hehe
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
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
 2 years ago

brinetheryBest ResponseYou've already chosen the best response.2
okay well good night
 2 years ago

NodataBest ResponseYou've already chosen the best response.0
Hahaha thak you for bugging me then =P. Good night!
 2 years ago
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