## anonymous 4 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. anonymous

i think this will fail in terms of scaler multiplication

2. anonymous

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

3. anonymous

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

4. anonymous

no guarentees, but i think this is right.

5. 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.

6. 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.

7. 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 :-)

8. anonymous

yw

9. 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

10. anonymous

yes

11. anonymous

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

12. anonymous

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

13. anonymous

yup

14. anonymous

How long ago did you take linear algebra?

15. anonymous

Mmmm like 3 years.

16. anonymous

Did you solve this problem already?

17. anonymous

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

18. anonymous

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

19. 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.

20. anonymous

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

21. 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.

22. anonymous

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

23. anonymous

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

24. 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

25. anonymous

Sorry, I hope you'll get better.

26. anonymous

You get a medal for that, lol

27. anonymous

haha ty.

28. anonymous

I know that one. Its good.

29. anonymous

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

30. anonymous

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

31. 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.

32. anonymous

I just really suck at the notation and proofs.

33. anonymous

You can see it like a videogame.

34. anonymous

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

35. anonymous

will do.

36. anonymous

Well see you then, have a nice night.

37. 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.

38. anonymous

organic chemistry?

39. anonymous

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

40. anonymous

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

41. anonymous

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

42. anonymous

ohh, what are your career goals now?

43. anonymous

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

44. anonymous

Wooow I used to like it haha

45. anonymous

46. anonymous

why do you not like it now?

47. anonymous

I like it now

48. anonymous

oh I see

49. anonymous

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

50. anonymous

51. anonymous

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

52. anonymous

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

53. anonymous

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

54. 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.

55. anonymous

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

56. anonymous

Could you help me with chemistry?

57. anonymous

They're the same!!!!

58. anonymous

I think the apple's fructose

59. anonymous

But it's the saaaaame molecule lolz

60. anonymous

Ohh yeah, I'm so dumb =P

61. anonymous

I didn't mean it that way :-D

62. anonymous

but you get the idea

63. anonymous

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

64. anonymous

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

65. anonymous

I get lost pretty soon.

66. anonymous

I like those problems with finding limiting reactant. yeeeaaah

67. anonymous

But I HATE redox. hate hate hate.

68. anonymous

hahha me too.

69. anonymous

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

70. 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

71. anonymous

okay well good night

72. anonymous

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