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 3 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).
 3 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).

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satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3i think this will fail in terms of scaler multiplication

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3should have \[a(\overline{v}+\overline{w})=a\overline{v}+a\overline{w}\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3but \[a(f\oplus g)\neq af\oplus ag\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3no guarentees, but i think this is right.

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2Hey 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.

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3actaully 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.

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2Yeah 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 :)

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2Sorry 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

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

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

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

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

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

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

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.2I 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.

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

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.0Ohh 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.

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

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

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.2Here'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

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

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

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

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

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

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.2That'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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.2Even 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.2I will, I'm taking statics next quarter. And yes, I will try to bug you with the hardest linalg problems I can find :D

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

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