## brinethery 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).

1. satellite73

i think this will fail in terms of scaler multiplication

2. satellite73

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

3. satellite73

but $a(f\oplus g)\neq af\oplus ag$

4. satellite73

no guarentees, but i think this is right.

5. brinethery

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.

6. satellite73

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.

7. brinethery

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 :-)

8. satellite73

yw

9. brinethery

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

10. satellite73

yes

11. brinethery

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

12. No-data

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

13. brinethery

yup

14. brinethery

How long ago did you take linear algebra?

15. No-data

Mmmm like 3 years.

16. No-data

Did you solve this problem already?

17. brinethery

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

18. brinethery

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

19. brinethery

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.

20. No-data

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

21. No-data

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.

22. No-data

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

23. brinethery

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

24. brinethery

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

25. No-data

Sorry, I hope you'll get better.

26. brinethery

You get a medal for that, lol

27. No-data

haha ty.

28. No-data

I know that one. Its good.

29. brinethery

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

30. No-data

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

31. brinethery

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.

32. brinethery

I just really suck at the notation and proofs.

33. No-data

You can see it like a videogame.

34. No-data

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

35. brinethery

will do.

36. No-data

Well see you then, have a nice night.

37. brinethery

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

38. No-data

organic chemistry?

39. No-data

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

40. brinethery

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

41. brinethery

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

42. No-data

ohh, what are your career goals now?

43. brinethery

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

44. No-data

Wooow I used to like it haha

45. brinethery

46. brinethery

why do you not like it now?

47. No-data

I like it now

48. brinethery

oh I see

49. No-data

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

50. brinethery

51. No-data

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

52. No-data

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

53. brinethery

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

54. brinethery

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.

55. brinethery

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

56. No-data

Could you help me with chemistry?

57. brinethery

They're the same!!!!

58. No-data

I think the apple's fructose

59. brinethery

But it's the saaaaame molecule lolz

60. No-data

Ohh yeah, I'm so dumb =P

61. brinethery

I didn't mean it that way :-D

62. brinethery

but you get the idea

63. brinethery

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

64. No-data

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

65. No-data

I get lost pretty soon.

66. brinethery

I like those problems with finding limiting reactant. yeeeaaah

67. brinethery

But I HATE redox. hate hate hate.

68. No-data

hahha me too.

69. No-data

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

70. brinethery

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

71. brinethery

okay well good night

72. No-data

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