Question

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).

Answer 1

i think this will fail in terms of scaler multiplication

Answer 2

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

Answer 3

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

Answer 4

no guarentees, but i think this is right.

Answer 5

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.

Answer 6

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.

Answer 7

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 :-)

Answer 8

yw

Answer 9

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

Answer 10

yes

Answer 11

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

Answer 12

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

Answer 13

yup

Answer 14

How long ago did you take linear algebra?

Answer 15

Mmmm like 3 years.

Answer 16

Did you solve this problem already?

Answer 17

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

Answer 18

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

Answer 19

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.

Answer 20

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

Answer 21

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.

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

Sorry, I hope you'll get better.

Answer 26

You get a medal for that, lol

Answer 27

haha ty.

Answer 28

I know that one. Its good.

Answer 29

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

Answer 30

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

Answer 31

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.

Answer 32

I just really suck at the notation and proofs.

Answer 33

You can see it like a videogame.

Answer 34

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

Answer 35

will do.

Answer 36

Well see you then, have a nice night.

Answer 37

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

Answer 38

organic chemistry?

Answer 39

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

Answer 40

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

Answer 41

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

Answer 42

ohh, what are your career goals now?

Answer 43

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

Answer 44

Wooow I used to like it haha

Answer 45

what changed your mind

Answer 46

why do you not like it now?

Answer 47

I like it now

Answer 48

oh I see

Answer 49

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

Answer 50

Oh wow, pretty advanced

Answer 51

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

Answer 52

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

Answer 53

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

Answer 54

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.

Answer 55

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

Answer 56

Could you help me with chemistry?

Answer 57

They're the same!!!!

Answer 58

I think the apple's fructose

Answer 59

But it's the saaaaame molecule lolz

Answer 60

Ohh yeah, I'm so dumb =P

Answer 61

I didn't mean it that way :-D

Answer 62

but you get the idea

Answer 63

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

Answer 64

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

Answer 65

I get lost pretty soon.

Answer 66

I like those problems with finding limiting reactant. yeeeaaah

Answer 67

But I HATE redox. hate hate hate.

Answer 68

hahha me too.

Answer 69

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

Answer 70

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

Answer 71

okay well good night

Answer 72

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