## angela210793 Group Title Find all the soulutions possible ... 2 years ago 2 years ago

1. angela210793

using matrices |dw:1333988132875:dw|

2. angela210793

since |A"=0 can qe use KRONECKER-CAPELLI THEOREM i did smth like |dw:1333988210313:dw|

3. angela210793

|dw:1333988330791:dw| but latter using gauss i got |dw:1333988378631:dw|

4. angela210793

did i do smth wrong?? |dw:1333988426922:dw|

5. experimentX

seems like the first and the last plane are parallel.

6. angela210793

7. experimentX

when ever two planes are parallel, they do not have solution.

8. experimentX

first and the last.

9. experimentX

and two planes will give you infinite solution.

10. experimentX

a line to be exact.

11. angela210793

wht will b the soluyions??? can u find them Experiment?

12. angela210793

solutions****

13. eliassaab

k=1, the last equation will be -2 times the first one The solutions lie on the line of intersections of the last two plane.

14. experimentX

you will have infinite solutions, substitute z from second and third.

15. experimentX

that will be a line, and line has infinite points. even if the first and the last line were not parallel, you were going to have infinite solution, because 4 variables and 3 equations---> that usually ends up that way.

16. angela210793

noo..k is a costant

17. experimentX

because you are free to choose any value of k, ... and for particular value of k, you will have particular solution.

18. experimentX

your solution WOULD have been in terms of k (that what i meant by infinite).

19. angela210793

lemme think a lil bit please

20. angela210793

tht's wht i did by using Kroneker-capelli....but the prob is that i get 0+0+0=2 at the last equation.... maybe i am being too dumb but i am really not getting it

21. experimentX

says that A must have same rank as [A|b]

22. experimentX

23. angela210793

yes...since r(A)=2 r(Ab) must be 2 too right

24. experimentX

A has rank 2 i guess

25. angela210793

what language is that Experiment??? O.o

26. experimentX

it has rank two ... checked from soft. Croatian ... i don't understand too. i used google to translate.

27. experimentX

can you tell me what is [A|b] ??

28. angela210793

r(Ab)=4-4k at least tht's wht i found

29. angela210793

|dw:1333989679050:dw|

30. angela210793

r u getting anything?

31. experimentX

Nop .. I am not really quite into mathematics ... I am just experimental

32. angela210793

hmmm.....ok...:) Thanks anyway :D I appreciate it :))

33. experimentX

i couldn't understand what does [A|b] represent.

34. angela210793

Ab is the matrice formed by the constants before variables and the solutions |dw:1333990018496:dw|

35. angela210793

not soultions sorry..they r not called solutions..I'm just not finding the right word -_-

36. experimentX

oh .. yeah i remember doingnthat (thanks to you). let's see what can i do for any arbitrary value .

37. angela210793

@hoblos any idea???

38. experimentX

for k=5, we get rank 3

39. experimentX

okay i will check this value from -1000 to 1000

40. angela210793

no actually u get rang 3 for every k different from 1

41. experimentX

it seems that we get rank 2 for k = -1

42. angela210793

oh wait...did i go wrong by equaling 4-4k=2?????????? O.o...i think i shouldn't have done that

43. experimentX

I think i understand what's going on.

44. experimentX

LOL ... this is quite funny.

45. FoolForMath

I have never heard of KRONECKER-CAPELLI THEOREM.

46. experimentX

it's amazing to know that @ffm does not know something. http://lavica.fesb.hr/mat1/predavanja/node38.html

47. angela210793

my google doesn't translate tht -_-

48. eliassaab

$x = \frac 3 2 -z \quad y = \frac 1 2$ z can be any number

49. experimentX

use translate feature of chrome.

50. angela210793

Can u show me how u got that please @eliassaab ???

51. eliassaab

write x + y = 2 - z -2 x + 2 y = 2 z - 2 and solve the two equations with repect to x and y

52. hoblos

|dw:1333990759995:dw| this can be reduced to |dw:1333990839175:dw| to find solutions.. r(A) must be same as r(A|B) so -2+2k=0 ----> k=1 thus 2y=1 ---> y=1/2 x-1/2 + z = 1 x+z = 3/2

53. eliassaab

x + y = 2 - z -x + y = z - 1 add the two equation to get y=1/2 and then find x

54. hoblos

sorry... instead of (-2-2k) it is (-2+2k)

55. angela210793

But Hoblos don't u get |dw:1333991218301:dw|

56. angela210793

i got -2-2k O.o cause i tried this too

57. hoblos

mm i cant see the whole drawing!! always different from what?

58. angela210793

zero

59. angela210793

u know what....take the system and try solving it urself and ignore everything i've said

60. hoblos

it must be equals to zero in order to have solutions!

61. experimentX

for other values of k other than -1, we will have two parallel planes and one non parallel. means two lines. for k=-1, we have first plane = last pane, so we will have one line (I think this is what the theorem is trying to tell .... I did not understand anything)

62. angela210793

i think the solutions r depended on k for k=1 are the soluions tht u find wht abt for kdifferent from 1?/

63. FoolForMath

Can't we use the rank method?

64. hoblos

for k different than 1 we dont have solutions..

65. experimentX

@hoblos it's -1 i think

66. angela210793

tht's wht we're doing Fool...Kronecker-capelli :P u don't have solutions??? how??????

67. eliassaab

If $k\ne 1$, there is no solutions. If $k= 1$, there are infinite number of solutions that I listed before,

68. hoblos

why would it be -1 @experimentX ??!!

69. FoolForMath

Oh god! I only didn't knew the name

70. angela210793

@FoolForMath tht makes Anxhela happy :) now start solving it....I'm going crazyyyy!!!!!!!!! :P

71. experimentX

because when k=1, we will have two lines ... for system of three planes.

72. FoolForMath

But then I am not a Russian :P So I guess I can't blame my teacher

73. FoolForMath
74. angela210793

lol :D

75. hoblos

well.. considering the first equation and the last one.. x-y+z =k *(-2) -2x+2y-2z=-2 -2x+2y-2z=-2k -2x+2y-2z=-2 so k must be 1

76. eliassaab

You really do not need heavy Theorems to do a rather simple problem.

77. experimentX

i guess .. so i might have made computation mistake.

78. angela210793

@eliassaab this is how we solve it in my univ..... @experimentX @hoblos @FoolForMath @eliassaab thanks a lot for trying and willing to help me :) forget this question :) I'll think again and repost it :))) thanks :)

79. experimentX

damn;; my mistake was computational ... LOL A = [1, -1, 1, i; 1, 1, 1, 2; -2, 2, -2, 2]; should have been -2 at the end.

80. hoblos

i remembred something we used to do... when r(A|B) < number of variables... we have no exact solutions.. instead we use a parameter so we take z=m this gives x= 3/2 -m so the solution is (3/2 -m, 1/2 , m) for any m belong to R