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I'm not sure what it is but this should give u a head start to what it means http://en.wikipedia.org/wiki/Column_space
wht i do not understand is how u make the transformations ...how do u know tht u change the places of x-row with y row...:(:(:(
To find the range of a matrix, just reduce it into row echelon form, and count the number of non zero rows. The number of non zero rows is the range of the matrix
Oh! that thing, I am afraid you will have to figure that out yourself.
But the key is to practice more and more reduction..
myself????? :O I've tried to...but i don't get it :((((
I can help you out with a rough algorithm or something like "steps to perform", but still you will need to practice using that algorithm.
ok....can u explain me how u solve aproblem like this in twiddla??
Why not here..?
But before that let me make sure, you want me to teach you how to reduce a matrix into row echelon form, right?
yea ok ....
So will I post an example? Or you will post yours
I'll post one |dw:1329561659776:dw|
OK, now tell me what do you feel you must first do, and why?
I have no idea at all :(((
OK, now you have to reduce it to something like |dw:1329561739686:dw|
With zeros in all the empty spaces, right?
yea tht's smth i know...
So start by making the top left corner 1
You can do that by two methods, 1. Bring the lowest row to the top, 2. Divide the first column by 3
The first method seems easy
I just exchanged row 1, and row 3
now u have to make 4 in the 3rd row 1 right?
Oh no, there is another, just let me write it fresh...
what happened to the 2 at the right corner?
Now again think, to make this new matrix similar to |dw:1329562260442:dw|
.....you need to make the first element in the 2nd row zero.
i think u'll get a |dw:1329562374039:dw| won't you???
i.e. the circled element |dw:1329562329966:dw|
Sorry, you lost me.. but did you understand what I meant?
yea yea i understood xD just tell me smth u make a diagonal =1 first and then 0 the other elements??
So the next step would be to subtract 2 times row-1 from row-2. Could you follow me?
I mean do you feel why I am doing that?
no.....don't u have to make the 4 in the third row 0 first???? O.o
Which one? Can you circle it for me?
No, not at all. All you need to do is keep in mind the picture I gave you and proceed accordingly
By picture I meant, the matrix with 1 on the diagonals and 0s elsewhere.
see.... wht u gave me is |dw:1329562830135:dw| and u have 4 ones in there(a diagonal with 4 elements) ...this isn't a square matrix to get tht....O.o and u said u'd do 1(ones) all the elements of the diagonal first then 0 the other elements......
I am sorry, if you got that impression, but that is not exactly what I meant. I meant something of that sort that doesn't necessarily imply that it has to be 4 squared etc etc.
I mean after reduction your picture will look something like that funny picture.
ahhhhhhhhhhhhhhhaaaaaaaaaaaaaaa......I'm sorry then :/ keep going....why would u multiply first row with 2 and then subtract it to row 2
Just to make it look like that funny picture...
You will end up with something like |dw:1329563098194:dw|
tht's wht i meant by this pic |dw:1329563199692:dw|
So what do you feel? Don't you feel that once you have got the first element in the first row 1, you should now start thinking about making the one just below it zero.
I really don't understand that notation of yours, but do you understand mine?
hahhaha...yea yea xD
So just tell me, do you feel why I want to make the element just below 1, zero?
sorry to barge in but is it just any diagonal or just the diagonal that cuts through starting with the first number?
i mean the diagonal that must be all 1's....
yes yes I get this I'm gonna ask u smth just pls don't get angry....don't u have to make |dw:1329563400348:dw| this 1 first????
Well, I never learnt it that way...:)
May be that is some other method.
ahhhhaaaaaaaaaa...ok then...u do wht u know...:)
math is a very clumsy road, u end up at the same destination
i wasn't ending up anywhere with this problem :P
did u read the manual/instruction/algorithm to solving this problem?
Is that clear?
wht did u do in there?????
OMG!!! I'm hopeless x( :(:(
got it or not?
wasn't the first element of the 2nd row supposed to b zero??? 2-(2*1)=2-2=0
Oh, does that thing look like 6, its actually 0..
ahhhhaaaaa...ok then xD
Next you need to turn the first element in the third row equal to zero
would tht be R3-3R1???
wait so u do 1 0 0 column by column, as in one column after the other?
Sasogeek is right!
1000 0100 0010 u should end up with this... right?
Exactly, but it may look a little different, but something similar to that.. P.S. angela210793 you typed the right notation
ok....no now u have to make -3 in the 2nd column zero...how do u do tht???
First of all, can you check, if I did the calculations correct?
Thats right! I think
i think so too O.o.....wht's next?
So the matrix which we now have is |dw:1329564404847:dw|
Now this particular problem was prepared in such a way, that we ended up with the 2nd and third row as equal
But that is a nice case, it will not happen always.
In cases where it doesn't happen, you next intention would be to make the circled element equal to 1|dw:1329564569074:dw|
Once the circle element is made 1, you will attempt to make all the elements below it equal to 0
can we multiply the second row with 1/7???
Yes, that is exactly what you should have done if you were a computer.
can.. but it would be complicated
try avoiding fractions form..
then what?? O.o
But being a human you can see, that you can subtract the second row from the third, and write it down in the third row
And that will make the whole of third row equal to zero
ohhhhhh...well i'm not a random person...I think like a computer :P
7 is still 7...wht now?
So now clearly you have two non zero rows, you can now say, that the range is 2
:O wht??? how was tht ..can u explain me once again please ???
ops it is R3=R3-R2
Just as I told you this was a nice problem. Real problems won't be like this. Here without any further reduction, it is visible, that no matter what you do, you can never make any of R2 or R1 zero... so there are two non zero rows. so t he range is 2
Hmmmmmmmmmmmm......ok.... Thank u very much :))))))))))) all of u, especially 2bornot2b :)) Gosh...How can u b so patient????
i dont understand what is range?
i don't think it is good :P
I meant it gives you the feel of what you need to do in real problems
ok now i understad what is range.. :)
And you can see in the reduction, things go in the same algorithm as I mentioned
so for the attachement given.. the range is 3 right?
ok now i understand.. but what it is for?
Something very deep xilem, its for actually solving linear equation.
yea...why do we need these kind of problems in business? O.o
But now it seems like a game
quoted earlier( wht i do not understand is how u make the transformations ...how do u know tht u change the places of x-row with y row...:(:(:( ) -this is call transpose
Say I have 10 equations and each equations have 10 unknown, how are you going to solve it?
so after having done all these things, I mean whatever you are studying, you will be able to solve linear equations without any effort.
i know wht transposed matrix is....i didn't know why u changed x with y and why not x with z for example
crammer's rule :D
But how did crammer invent that? This is all behind the scenes
i think all these things r unnecessary.....
I'm going to do my hws now...hopefully i'll solve them :) thnx a lot :)
hurmm... sorry can u show me example of that in cramers rule?
I said that you learn linear algebra to be able to solve linear equations, and cramers rule is just a product of linear algebra, so it directly is not a problem which can be used to show the application of cramers rule.
no i mean for the cramers rule (.i didn't know why u changed x with y and why not x with z for example ) can u show me example?
this is how I've been taught cramer's rule |dw:1329576915751:dw|