angela210793
  • angela210793
Matrix
Mathematics
schrodinger
  • schrodinger
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angela210793
  • angela210793
I thought to multiply the first row with 1/3...|dw:1329578934017:dw|
nenadmatematika
  • nenadmatematika
that would be a good idea angela :D
angela210793
  • angela210793
i can make the first element in the second row 0 but i can't go further :(

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bahrom7893
  • bahrom7893
what's r? reduced row echelon?
angela210793
  • angela210793
idk wht u call it...i'm asking for the range
nenadmatematika
  • nenadmatematika
why? multiply the first row with -4 and add to the third row to get 0 under
amistre64
  • amistre64
colA is the range of a matrix A right?
amistre64
  • amistre64
row reduce to determine your pivot points; and all columns with a pivot point define colA
angela210793
  • angela210793
I'm sorry i don't get it..wht is colA???
amistre64
  • amistre64
as far as I can tell, thats the american version of range of a matrix
nenadmatematika
  • nenadmatematika
|dw:1329579146175:dw|
amistre64
  • amistre64
can you type in the rows? a b c d e f g h like that cause its hard to read .... well, nenands is a bit clearer
nenadmatematika
  • nenadmatematika
|dw:1329579294854:dw|
amistre64
  • amistre64
your matrix I believe will simplify to 3 linearly independant column vectors; or less. that will tell us the range or span
angela210793
  • angela210793
:O:O:O:O How nenad?????? in the example my teacher has solved she has had the elements of the diagonal =1 :O
angela210793
  • angela210793
has made***
amistre64
  • amistre64
turning it into row reduced is extra work becasue the pivots dont change
nenadmatematika
  • nenadmatematika
no Angela I'm sure this is the solution...it's quite easy...do you know the procedure to get the rank of the matrix?
angela210793
  • angela210793
i know the theory but i don't know how to use tht in practice -_-
angela210793
  • angela210793
how did u know u should have changed R1with R3???
nenadmatematika
  • nenadmatematika
well this is how you start...first you take a look at the first element of the matrix (first row and the first column)....if it's different from zero then you call it ''the pivot''. OK? Now you make zeros under that first pivot using muliplication with some number and adding to the row below....that's how you make the zeros under the first pivot. Then you look for another pivot...you follow the main diagonal and if it's different from zero then it's a second pivot and you make zeros under that number...you continue with this procedure until you're finished....the final rank is the number of elements on the main diagonal different from zero, so the number of pivots...in this case I have three pivots so the rank is 3
angela210793
  • angela210793
Hmmmm.....ok thanks guys :):)
nenadmatematika
  • nenadmatematika
>> rank([3 6 9 3;2 -5 3 0;4 -10 10 4]) ans = 3
nenadmatematika
  • nenadmatematika
Matlab says it's 3 also so your teacher is tripping :D
angela210793
  • angela210793
I'm really hopeless...:(:( thank you very much :) both of u :)
nenadmatematika
  • nenadmatematika
angela don't go...I can show you some examples so you can learn the procedure? I can give you some matrix and we'll work on it together OK?
angela210793
  • angela210793
yes yes yes :)
nenadmatematika
  • nenadmatematika
ok here is one for begining:|dw:1329580248289:dw|
nenadmatematika
  • nenadmatematika
now tell me what is the first element of this matrix and is it different from zero?
angela210793
  • angela210793
since the first element f the matrix is 1 then the first element of R2 must be 0???
angela210793
  • angela210793
is the rank 1?? O.o
angela210793
  • angela210793
range***
nenadmatematika
  • nenadmatematika
OK it's 1...so that is the first pivot...now do some operations to make 0 under that 1....the easiest way is to multiply the first row with -3 and to the second row...draw that so I can see OK?
nenadmatematika
  • nenadmatematika
add*
angela210793
  • angela210793
|dw:1329580611324:dw|
nenadmatematika
  • nenadmatematika
that's great...now since you made zero under that 1, the next step is to look for the next pivot(element different from zero) on the main diagonal....it's number -2....so you have to make zeros under that pivot...but since there are no more elements under that -2 the transformations are done and now you can read the rank of the matrix....the rank is the number of row where at least one element is different from zero, or you can count the number of pivots(elements on the main diagonal different from zero)...so what is the rank?
RagingSquirrel
  • RagingSquirrel
*Clicks on question thinking it's about the matrix* DANGIT
nenadmatematika
  • nenadmatematika
number of rows*
angela210793
  • angela210793
so the range is 2???
nenadmatematika
  • nenadmatematika
correct Angela!!! :D just to be clear here in Serbia we call it rang, but I read this material from the American matematicians and I'm sure they use the term ''rank''
angela210793
  • angela210793
haha :) can we work on some more examples pleaseeeee
nenadmatematika
  • nenadmatematika
of course....check this one:|dw:1329580900431:dw|
angela210793
  • angela210793
|dw:1329581058847:dw|
nenadmatematika
  • nenadmatematika
yes :D
angela210793
  • angela210793
|dw:1329581078055:dw|
nenadmatematika
  • nenadmatematika
no...we must make a deal here....it's very important the way you make zeros...you can't do it anyway you want...first you make the zeros under that 1. So multiply the first row with -2 and add to the second row....in the third row you already have zero so you don't touch that third row OK.? draw again...:D
angela210793
  • angela210793
no way :(:(|dw:1329581327917:dw|
nenadmatematika
  • nenadmatematika
great it's correct now what is the next pivot you see?
angela210793
  • angela210793
10????
nenadmatematika
  • nenadmatematika
that's my girl....now make zeros under that pivot....
angela210793
  • angela210793
xD just a thought...how abt R1-2R3???
angela210793
  • angela210793
tht won't work will it???
nenadmatematika
  • nenadmatematika
you don't touch the first row anymore...you made zeros under the first pivot, so you now operate with the second row....for example multiply the second pivot with -1/5 and add to the third row...
nenadmatematika
  • nenadmatematika
|dw:1329581919090:dw|
angela210793
  • angela210793
|dw:1329582143630:dw|
nenadmatematika
  • nenadmatematika
what is the third pivot now?
angela210793
  • angela210793
5??? but there's no 0 under it O.o
nenadmatematika
  • nenadmatematika
that's right....that means no more transformations with the matrix so what is the rank?
angela210793
  • angela210793
3??
nenadmatematika
  • nenadmatematika
yes
angela210793
  • angela210793
ur a genius xD :) Can i borrow ur brain???????
nenadmatematika
  • nenadmatematika
wait we must do one more :D
angela210793
  • angela210793
sure :)))
nenadmatematika
  • nenadmatematika
|dw:1329582383881:dw|
nenadmatematika
  • nenadmatematika
haha :D
angela210793
  • angela210793
how abt R1-2R3???
nenadmatematika
  • nenadmatematika
no problem :D OK Angela what is the first number you see?
angela210793
  • angela210793
|dw:1329582684252:dw|
angela210793
  • angela210793
OMG wait.... will i be the stupid girl who didn't get a single thing? :O:O:O
nenadmatematika
  • nenadmatematika
OK I hope we both agree that is unconvenient to perform ''zero making'' under that 13...so one of the possibilities is to exchange the first and the third column because the third column is filled with ''beautiful numbers '' for addition, multiplication etc do it
angela210793
  • angela210793
i was just going to ask if we could change C3 with C1 :)
angela210793
  • angela210793
|dw:1329582859078:dw|
nenadmatematika
  • nenadmatematika
now you work and I watch....:D
angela210793
  • angela210793
|dw:1329582907187:dw|
nenadmatematika
  • nenadmatematika
|dw:1329582876260:dw|
angela210793
  • angela210793
|dw:1329583007088:dw|
angela210793
  • angela210793
ahhhhaaaa...i just wanted ur confirmation ;) :P
angela210793
  • angela210793
|dw:1329583049393:dw|
nenadmatematika
  • nenadmatematika
|dw:1329583024634:dw|
angela210793
  • angela210793
|dw:1329583163929:dw|
nenadmatematika
  • nenadmatematika
|dw:1329583152017:dw|