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brinethery Group Title

Linear Algebra: Determine whether this is a vector space. Either show that the necessary properties are satisfied, or give an example that at least one of them is not. -The set of all upper-triangular m x n matrices

  • 2 years ago
  • 2 years ago

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  1. brinethery Group Title
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    Ah, I just don't get this stuff!

    • 2 years ago
  2. Pippa Group Title
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    hehe wait a sec i am just checking :)

    • 2 years ago
  3. KingGeorge Group Title
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    I'm pretty sure this is a vector space since it satisfies all the axioms need for a vector space.

    • 2 years ago
  4. Pippa Group Title
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    it is a vector space that is forsure

    • 2 years ago
  5. Pippa Group Title
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    you just have to go thru all the axioms which is a pain :)

    • 2 years ago
  6. Pippa Group Title
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    umm i wonder if you can assign values to the matrix to show that all axioms are true or you just have to leave them as variables

    • 2 years ago
  7. Pippa Group Title
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    umm if you show using real values it is easier

    • 2 years ago
  8. Pippa Group Title
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    but i am not sure what ur prof wld want

    • 2 years ago
  9. brinethery Group Title
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    It would probably have to be more formal mathematical language... he docked me when I was doing a proof with a 3x3 matrix one time.

    • 2 years ago
  10. KingGeorge Group Title
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    All you would really need to show is that the set of upper triangular matrices is closed under addition which is obvious. The other axioms are properties of matrices, or follow directly from closure of addition.

    • 2 years ago
  11. Pippa Group Title
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    well i doubt her prof wld accepy that :)

    • 2 years ago
  12. Pippa Group Title
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    anyways if its closed under addition not neccesairy will it be cllosed under multiplication

    • 2 years ago
  13. KingGeorge Group Title
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    Well, closure of addition implies that u+v is still a matrix, if u, v are upper-triangular matrices. Since addition is associative, and multiplying matrices by scalars is a property of matrices that is well-defined, all the axioms are satisfied. In a vector space, you never multiply vectors together.

    • 2 years ago
  14. Pippa Group Title
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    kk but she still has to show that all the axioms are satisfied

    • 2 years ago
  15. KingGeorge Group Title
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    Yes, but their proof are almost trivial once you've showed closure of addition.

    • 2 years ago
  16. Pippa Group Title
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    True :)

    • 2 years ago
  17. Pippa Group Title
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    umm brinethy u know how to show that all the 10 axioms r true?

    • 2 years ago
  18. brinethery Group Title
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    I don't know how to do this with a general mxn matrix

    • 2 years ago
  19. brinethery Group Title
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    showing that it's closed under scalar multiplication and vector addition, I mean.

    • 2 years ago
  20. Pippa Group Title
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    give me a sec and i will do it

    • 2 years ago
  21. KingGeorge Group Title
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    Scalar multiplication should already be given to you as a property of matrices. As for vector addition, choose two arbitrary m x n upper triangular matrices, and add them together. It should become pretty obvious that it's closed after that.

    • 2 years ago
  22. brinethery Group Title
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    Pippa, thank you very much for taking the time to do this for me. I can't tell you how much I appreciate it.

    • 2 years ago
  23. Pippa Group Title
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    • 2 years ago
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  24. Pippa Group Title
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    well i just proved that they are closed under addition and scaler multiplication. Do u see how?

    • 2 years ago
  25. KingGeorge Group Title
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    Aren't those all lower triangular matrices? not upper?

    • 2 years ago
  26. Pippa Group Title
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    oh Sh* but it wld be the same thing

    • 2 years ago
  27. Pippa Group Title
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    its a good thing u r around king

    • 2 years ago
  28. KingGeorge Group Title
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    no problem at all.

    • 2 years ago
  29. Pippa Group Title
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    umm there are still 8 more axioms that need to be proved

    • 2 years ago
  30. Pippa Group Title
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    some of them take much longer to prive than others

    • 2 years ago
  31. Pippa Group Title
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    These are the two main ones

    • 2 years ago
  32. Pippa Group Title
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    R u still there?

    • 2 years ago
  33. brinethery Group Title
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    Yeah, I stepped out. My dad had to tell me something

    • 2 years ago
  34. brinethery Group Title
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    I'm opening your file right now

    • 2 years ago
  35. Pippa Group Title
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    lol that is ok:)

    • 2 years ago
  36. brinethery Group Title
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    So as long as it's closed under vector addition and scalar multiplication, the set is a vector space?

    • 2 years ago
  37. Pippa Group Title
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    umm well u kind of have to prove the other axioms as well which is harder

    • 2 years ago
  38. Pippa Group Title
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    and btw by accident i proved using lower traingles in stead of upper

    • 2 years ago
  39. brinethery Group Title
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    Yes, I am aware of that

    • 2 years ago
  40. KingGeorge Group Title
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    While you have to show a little more, the only other part that doesn't follow directly from those facts is that you need to find an inverse matrix (hint: multiply by -1 to get the inverse)

    • 2 years ago
  41. Pippa Group Title
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    y wld u need to do that?

    • 2 years ago
  42. Pippa Group Title
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    I am just wondering cuz i dont remember ever doing that?

    • 2 years ago
  43. Pippa Group Title
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    idk I just went thru every axiom

    • 2 years ago
  44. brinethery Group Title
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    Sorry guys, I am even more lost. I guess you have to go through all the axioms but I'm not getting a clear answer. I'll ask the instructor tomorrow, but he'll probably confuse me even more lol

    • 2 years ago
  45. Pippa Group Title
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    LOL yes well you just went thru two axioms you just proved that it is closed under addition and that it is closed under scaler mutiplication

    • 2 years ago
  46. Pippa Group Title
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    Like in ur textbook there shld be another 8 axioms that need to be proved liek one of them is u+v = v+u and (u+v)+w=u+(w+v) and many others

    • 2 years ago
  47. Pippa Group Title
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    but it will take me hours to write them out unfortunately i dont have a tablet so like maybe ask ur prof to show u how

    • 2 years ago
  48. Pippa Group Title
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    k gonna go study i hope i was a lil bit helpful :)

    • 2 years ago
  49. brinethery Group Title
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    I will. And I really appreciate your help, thank you for taking the time to explain this stuff to me.

    • 2 years ago
  50. Pippa Group Title
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    U r welcome its fun to teach others cuz that means I am comfortable enough in this area to explain it to others :) Gluck

    • 2 years ago
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