anonymous
  • anonymous
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)
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
I am learning linear algebra as well, can you tell me what topic this comes from ?
anonymous
  • anonymous
determining is v is a vector space... so we have to verify the ten axioms
anonymous
  • anonymous
so we are finding what order space this is?

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anonymous
  • anonymous
mm.. what u mean with order space?
anonymous
  • anonymous
line plane is 2nd order space, line is 1st order space
anonymous
  • anonymous
ohhh,,, well my example is already i 3 space
anonymous
  • anonymous
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
anonymous
  • anonymous
2)scalar multiplication***
anonymous
  • anonymous
I know about first two , but never heard of this '10 axioms' stuff
anonymous
  • anonymous
are you learning it independently or with class?
anonymous
  • anonymous
class
anonymous
  • anonymous
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
anonymous
  • anonymous
so in this case im trying to verify number 8
anonymous
  • anonymous
distributive property
anonymous
  • anonymous
kind of
anonymous
  • anonymous
do you watch MIT lectures
anonymous
  • anonymous
mmm nop
anonymous
  • anonymous
are u learning independenly
anonymous
  • anonymous
yes
anonymous
  • anonymous
ohh
anonymous
  • anonymous
I tend to do better in class , if I already learned it beforehand
anonymous
  • anonymous
have you done differential equation yet?
anonymous
  • anonymous
yes in calculus..
anonymous
  • anonymous
im learning it now
anonymous
  • anonymous
let me know if you need any help with differential equation; I am really good at it
anonymous
  • anonymous
:).. 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
anonymous
  • anonymous
no, I just finished the class this semseter
anonymous
  • anonymous
so u r good with double and triples integrals too?
mathmate
  • mathmate
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

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