Find all the soulutions possible ...

- angela210793

Find all the soulutions possible ...

- schrodinger

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- angela210793

using matrices |dw:1333988132875:dw|

- angela210793

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

- angela210793

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

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## More answers

- angela210793

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

- experimentX

seems like the first and the last plane are parallel.

- angela210793

which???? show me please

- experimentX

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

- experimentX

first and the last.

- experimentX

and two planes will give you infinite solution.

- experimentX

a line to be exact.

- angela210793

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

- angela210793

solutions****

- anonymous

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.

- experimentX

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

- 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.

- angela210793

noo..k is a costant

- experimentX

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

- experimentX

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

- angela210793

lemme think a lil bit please

- 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

- experimentX

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

- experimentX

use google translate
http://lavica.fesb.hr/mat1/predavanja/node38.html

- angela210793

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

- experimentX

A has rank 2 i guess

- angela210793

what language is that Experiment??? O.o

- experimentX

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

- experimentX

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

- angela210793

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

- angela210793

|dw:1333989679050:dw|

- angela210793

r u getting anything?

- experimentX

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

- angela210793

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

- experimentX

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

- angela210793

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

- angela210793

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

- experimentX

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

- angela210793

@hoblos any idea???

- experimentX

for k=5, we get rank 3

- experimentX

okay i will check this value from -1000 to 1000

- angela210793

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

- experimentX

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

- angela210793

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

- experimentX

I think i understand what's going on.

- experimentX

LOL ... this is quite funny.

- anonymous

I have never heard of KRONECKER-CAPELLI THEOREM.

- experimentX

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

- angela210793

my google doesn't translate tht -_-

- anonymous

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

- experimentX

use translate feature of chrome.

- angela210793

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

- anonymous

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

- 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

- anonymous

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

- hoblos

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

- angela210793

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

- angela210793

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

- hoblos

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

- angela210793

zero

- angela210793

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

- hoblos

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

- 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)

- angela210793

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

- anonymous

Can't we use the rank method?

- hoblos

for k different than 1 we dont have solutions..

- experimentX

@hoblos it's -1 i think

- angela210793

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

- anonymous

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

- hoblos

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

- anonymous

Oh god! I only didn't knew the name

- angela210793

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

- experimentX

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

- anonymous

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

- anonymous

http://en.wikipedia.org/wiki/Rouch%C3%A9%E2%80%93Capelli_theorem

- angela210793

lol :D

- 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

- anonymous

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

- experimentX

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

- 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 :)

- 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.

- 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

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