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anilorap

LINEAR ALGEBRA. verifying (k+m)(u)=ku+mu... where k,m are any integers and u is an element of V={(x,y,z) | z=3}. addition defined by (x1,y1,z1)+(x2,y2,z2) = (x1+x2,y1+y2,3) scalar multiplication defined by s(x,y,z)=(sx,sy,3)

  • 2 years ago
  • 2 years ago

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  1. imranmeah91
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    I am learning linear algebra as well, can you tell me what topic this comes from ?

    • 2 years ago
  2. anilorap
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    determining is v is a vector space... so we have to verify the ten axioms

    • 2 years ago
  3. imranmeah91
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    so we are finding what order space this is?

    • 2 years ago
  4. anilorap
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    mm.. what u mean with order space?

    • 2 years ago
  5. imranmeah91
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    line plane is 2nd order space, line is 1st order space

    • 2 years ago
  6. anilorap
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    ohhh,,, well my example is already i 3 space

    • 2 years ago
  7. anilorap
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    if u already covered this section.. we defined vector space as a set of vectors on which are defined by two operations: 1) vector addition 2) vector multiplication and must satisfy 10 axioms

    • 2 years ago
  8. anilorap
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    2)scalar multiplication***

    • 2 years ago
  9. imranmeah91
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    I know about first two , but never heard of this '10 axioms' stuff

    • 2 years ago
  10. imranmeah91
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    are you learning it independently or with class?

    • 2 years ago
  11. anilorap
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    class

    • 2 years ago
  12. anilorap
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    1. u + v 2 V (V is closed under addition) 2. u + v = v + u (commutative property) 3. (u + v) + w = u + (v + w) (associative property) 4. There exists a vector in V , called the zero vector and denoted 0 such that u + 0 = u (additive identity) 5. For every vector u in V , there exists a vector 􀀀u also in V such that u + (􀀀u) = 0 (additive inverse) 6. cu 2 V (V is closed under scalar multiplication) 7. c (u + v) = cu + cv 8. (c + d) u = cu + du 9. c (du) = (cd) u 10. 1u = u

    • 2 years ago
  13. anilorap
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    so in this case im trying to verify number 8

    • 2 years ago
  14. imranmeah91
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    distributive property

    • 2 years ago
  15. anilorap
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    kind of

    • 2 years ago
  16. imranmeah91
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    do you watch MIT lectures

    • 2 years ago
  17. anilorap
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    mmm nop

    • 2 years ago
  18. anilorap
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    are u learning independenly

    • 2 years ago
  19. imranmeah91
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    yes

    • 2 years ago
  20. anilorap
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    ohh

    • 2 years ago
  21. imranmeah91
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    I tend to do better in class , if I already learned it beforehand

    • 2 years ago
  22. imranmeah91
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    have you done differential equation yet?

    • 2 years ago
  23. anilorap
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    yes in calculus..

    • 2 years ago
  24. anilorap
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    im learning it now

    • 2 years ago
  25. imranmeah91
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    let me know if you need any help with differential equation; I am really good at it

    • 2 years ago
  26. anilorap
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    :).. cool... i like derivative for some reasons... where im having a little trouble is in double and triple integrals... are u also learning that independnly

    • 2 years ago
  27. imranmeah91
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    no, I just finished the class this semseter

    • 2 years ago
  28. anilorap
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    so u r good with double and triples integrals too?

    • 2 years ago
  29. mathmate
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    Given u(x,y,z), (x1,y1,z1)+(x2,y2,z2) = (x1+x2,y1+y2,3) s(x,y,z)=(sx,sy,3) Assuming vector space is defined over field F such as R. (k+m)(u) =(k+m)(x,y,3) [definition of u] =((k+m)x,(k+m)y,3) [definition of scalar multiplication] =(kx+mx, ky+my,3) [distributivity defined over F] =(kx,ky,3)+(mx,my,3) [definition of addition] =k(x,y,3)+m(x,y,3) [definition of scalar multiplication] =ku+mu [definition of u] QED

    • 2 years ago
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