Matrix

- angela210793

Matrix

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- angela210793

I thought to multiply the first row with 1/3...|dw:1329578934017:dw|

- nenadmatematika

that would be a good idea angela :D

- angela210793

i can make the first element in the second row 0 but i can't go further :(

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## More answers

- bahrom7893

what's r? reduced row echelon?

- angela210793

idk wht u call it...i'm asking for the range

- nenadmatematika

why? multiply the first row with -4 and add to the third row to get 0 under

- amistre64

colA is the range of a matrix A right?

- amistre64

row reduce to determine your pivot points; and all columns with a pivot point define colA

- angela210793

I'm sorry i don't get it..wht is colA???

- amistre64

as far as I can tell, thats the american version of range of a matrix

- nenadmatematika

|dw:1329579146175:dw|

- 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

|dw:1329579294854:dw|

- amistre64

your matrix I believe will simplify to 3 linearly independant column vectors; or less. that will tell us the range or span

- 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

has made***

- amistre64

turning it into row reduced is extra work becasue the pivots dont change

- 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

i know the theory but i don't know how to use tht in practice -_-

- angela210793

how did u know u should have changed R1with R3???

- 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

Hmmmm.....ok thanks guys :):)

- nenadmatematika

>> rank([3 6 9 3;2 -5 3 0;4 -10 10 4])
ans =
3

- nenadmatematika

Matlab says it's 3 also so your teacher is tripping :D

- angela210793

I'm really hopeless...:(:(
thank you very much :) both of u :)

- 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

yes yes yes :)

- nenadmatematika

ok here is one for begining:|dw:1329580248289:dw|

- nenadmatematika

now tell me what is the first element of this matrix and is it different from zero?

- angela210793

since the first element f the matrix is 1 then the first element of R2 must be 0???

- angela210793

is the rank 1?? O.o

- angela210793

range***

- 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

add*

- angela210793

|dw:1329580611324:dw|

- 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

*Clicks on question thinking it's about the matrix*
DANGIT

- nenadmatematika

number of rows*

- angela210793

so the range is 2???

- 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

haha :) can we work on some more examples pleaseeeee

- nenadmatematika

of course....check this one:|dw:1329580900431:dw|

- angela210793

|dw:1329581058847:dw|

- nenadmatematika

yes :D

- angela210793

|dw:1329581078055:dw|

- 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

no way :(:(|dw:1329581327917:dw|

- nenadmatematika

great it's correct now what is the next pivot you see?

- angela210793

10????

- nenadmatematika

that's my girl....now make zeros under that pivot....

- angela210793

xD just a thought...how abt R1-2R3???

- angela210793

tht won't work will it???

- 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

|dw:1329581919090:dw|

- angela210793

|dw:1329582143630:dw|

- nenadmatematika

what is the third pivot now?

- angela210793

5???
but there's no 0 under it O.o

- nenadmatematika

that's right....that means no more transformations with the matrix so what is the rank?

- angela210793

3??

- nenadmatematika

yes

- angela210793

ur a genius xD :) Can i borrow ur brain???????

- nenadmatematika

wait we must do one more :D

- angela210793

sure :)))

- nenadmatematika

|dw:1329582383881:dw|

- nenadmatematika

haha :D

- angela210793

how abt R1-2R3???

- nenadmatematika

no problem :D OK Angela what is the first number you see?

- angela210793

|dw:1329582684252:dw|

- angela210793

OMG wait.... will i be the stupid girl who didn't get a single thing? :O:O:O

- 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

i was just going to ask if we could change C3 with C1 :)

- angela210793

|dw:1329582859078:dw|

- nenadmatematika

now you work and I watch....:D

- angela210793

|dw:1329582907187:dw|

- nenadmatematika

|dw:1329582876260:dw|

- angela210793

|dw:1329583007088:dw|

- angela210793

ahhhhaaaa...i just wanted ur confirmation ;) :P

- angela210793

|dw:1329583049393:dw|

- nenadmatematika

|dw:1329583024634:dw|

- angela210793

|dw:1329583163929:dw|

- nenadmatematika

|dw:1329583152017:dw|

- angela210793

|dw:1329583287374:dw|

- angela210793

Thank you Nenad :)))))))))))))))))))))))))

- nenadmatematika

there is one more detail....one small detail....check this out:|dw:1329583260489:dw|

- angela210793

|dw:1329583412739:dw|

- angela210793

can we change R2 with R3??

- nenadmatematika

that's my girl.....the zero cannot be pivot, so the next step is to look below zero to see if you can find non-zero element...if it's different from zero, switch second and the third row and the problem solved :D

- angela210793

I love u Nenad ^_^ |dw:1329583700245:dw|