Is there anyone who can explain me the range of a matrix???

- angela210793

Is there anyone who can explain me the range of a matrix???

- chestercat

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- sasogeek

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

- angela210793

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...:(:(:(

- 2bornot2b

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

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## More answers

- 2bornot2b

Oh! that thing, I am afraid you will have to figure that out yourself.

- 2bornot2b

But the key is to practice more and more reduction..

- angela210793

myself????? :O I've tried to...but i don't get it :((((

- 2bornot2b

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.

- angela210793

ok....can u explain me how u solve aproblem like this in twiddla??

- 2bornot2b

Why not here..?

- 2bornot2b

But before that let me make sure, you want me to teach you how to reduce a matrix into row echelon form, right?

- angela210793

yea ok ....

- 2bornot2b

So will I post an example? Or you will post yours

- angela210793

I'll post one |dw:1329561659776:dw|

- 2bornot2b

OK, now tell me what do you feel you must first do, and why?

- angela210793

I have no idea at all :(((

- 2bornot2b

OK, now you have to reduce it to something like |dw:1329561739686:dw|

- 2bornot2b

With zeros in all the empty spaces, right?

- angela210793

yea tht's smth i know...

- 2bornot2b

So start by making the top left corner 1

- 2bornot2b

You can do that by two methods,
1. Bring the lowest row to the top,
2. Divide the first column by 3

- 2bornot2b

The first method seems easy

- 2bornot2b

I just exchanged row 1, and row 3

- angela210793

now u have to make 4 in the 3rd row 1 right?

- 2bornot2b

Oh no, there is another, just let me write it fresh...

- sasogeek

what happened to the 2 at the right corner?

- angela210793

|dw:1329562219705:dw|

- 2bornot2b

|dw:1329562156101:dw|

- 2bornot2b

Right!

- 2bornot2b

Now again think, to make this new matrix similar to |dw:1329562260442:dw|

- 2bornot2b

.....you need to make the first element in the 2nd row zero.

- angela210793

i think u'll get a |dw:1329562374039:dw| won't you???

- 2bornot2b

i.e. the circled element |dw:1329562329966:dw|

- 2bornot2b

Sorry, you lost me.. but did you understand what I meant?

- angela210793

yea yea i understood xD
just tell me smth u make a diagonal =1 first and then 0 the other elements??

- 2bornot2b

Right!

- 2bornot2b

So the next step would be to subtract 2 times row-1 from row-2. Could you follow me?

- 2bornot2b

I mean do you feel why I am doing that?

- angela210793

no.....don't u have to make the 4 in the third row 0 first???? O.o

- 2bornot2b

Which one? Can you circle it for me?

- angela210793

|dw:1329562705396:dw|

- 2bornot2b

No, not at all. All you need to do is keep in mind the picture I gave you and proceed accordingly

- 2bornot2b

By picture I meant, the matrix with 1 on the diagonals and 0s elsewhere.

- angela210793

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......

- 2bornot2b

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.

- 2bornot2b

I mean after reduction your picture will look something like that funny picture.

- angela210793

ahhhhhhhhhhhhhhhaaaaaaaaaaaaaaa......I'm sorry then :/ keep going....why would u multiply first row with 2 and then subtract it to row 2

- 2bornot2b

Just to make it look like that funny picture...

- 2bornot2b

You will end up with something like
|dw:1329563098194:dw|

- angela210793

tht's wht i meant by this pic |dw:1329563199692:dw|

- 2bornot2b

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.

- 2bornot2b

I really don't understand that notation of yours, but do you understand mine?

- 2bornot2b

;)

- angela210793

hahhaha...yea yea xD

- 2bornot2b

So just tell me, do you feel why I want to make the element just below 1, zero?

- sasogeek

sorry to barge in but is it just any diagonal or just the diagonal that cuts through starting with the first number?

- sasogeek

i mean the diagonal that must be all 1's....

- 2bornot2b

Any diagonal...

- angela210793

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????

- 2bornot2b

Well, I never learnt it that way...:)

- 2bornot2b

May be that is some other method.

- angela210793

ahhhhaaaaaaaaaa...ok then...u do wht u know...:)

- sasogeek

math is a very clumsy road, u end up at the same destination

- angela210793

i wasn't ending up anywhere with this problem :P

- sasogeek

did u read the manual/instruction/algorithm to solving this problem?

- 2bornot2b

|dw:1329563439879:dw|

- 2bornot2b

Is that clear?

- angela210793

wht did u do in there?????

- angela210793

OMG!!! I'm hopeless x( :(:(

- 2bornot2b

R2-2R1

- 2bornot2b

got it or not?

- angela210793

wasn't the first element of the 2nd row supposed to b zero???
2-(2*1)=2-2=0

- 2bornot2b

Oh, does that thing look like 6, its actually 0..

- 2bornot2b

lol

- angela210793

ahhhhaaaaa...ok then xD

- 2bornot2b

Next you need to turn the first element in the third row equal to zero

- angela210793

would tht be R3-3R1???

- sasogeek

wait so u do 1 0 0 column by column, as in one column after the other?

- 2bornot2b

|dw:1329563860051:dw|

- 2bornot2b

Sasogeek is right!

- sasogeek

1000
0100
0010
u should end up with this... right?

- 2bornot2b

Exactly, but it may look a little different, but something similar to that..
P.S. angela210793 you typed the right notation

- angela210793

ok....no now u have to make -3 in the 2nd column zero...how do u do tht???

- 2bornot2b

First of all, can you check, if I did the calculations correct?

- angela210793

hang on

- angela210793

|dw:1329564323164:dw|

- 2bornot2b

Thats right! I think

- angela210793

i think so too O.o.....wht's next?

- 2bornot2b

So the matrix which we now have is |dw:1329564404847:dw|

- 2bornot2b

Now this particular problem was prepared in such a way, that we ended up with the 2nd and third row as equal

- 2bornot2b

But that is a nice case, it will not happen always.

- 2bornot2b

In cases where it doesn't happen, you next intention would be to make the circled element equal to 1|dw:1329564569074:dw|

- 2bornot2b

Once the circle element is made 1, you will attempt to make all the elements below it equal to 0

- angela210793

can we multiply the second row with 1/7???

- 2bornot2b

Yes, that is exactly what you should have done if you were a computer.

- anonymous

can.. but it would be complicated

- anonymous

try avoiding fractions form..

- angela210793

then what?? O.o

- 2bornot2b

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

- 2bornot2b

And that will make the whole of third row equal to zero

- angela210793

ohhhhhh...well i'm not a random person...I think like a computer :P

- 2bornot2b

|dw:1329564788814:dw|

- angela210793

7 is still 7...wht now?

- 2bornot2b

So now clearly you have two non zero rows, you can now say, that the range is 2

- anonymous

R3=R3+R2

- angela210793

:O wht??? how was tht ..can u explain me once again please ???

- anonymous

ops it is R3=R3-R2

- 2bornot2b

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

- angela210793

Hmmmmmmmmmmmm......ok....
Thank u very much :))))))))))) all of u, especially 2bornot2b :)) Gosh...How can u b so patient????

- anonymous

i dont understand what is range?

- 2bornot2b

Here is a good problem

##### 1 Attachment

- angela210793

i don't think it is good :P

- 2bornot2b

I meant it gives you the feel of what you need to do in real problems

- anonymous

ok now i understad what is range.. :)

- 2bornot2b

And you can see in the reduction, things go in the same algorithm as I mentioned

- anonymous

so for the attachement given.. the range is 3 right?

- 2bornot2b

Right xilem

- anonymous

ok now i understand.. but what it is for?

- 2bornot2b

Something very deep xilem, its for actually solving linear equation.

- angela210793

yea...why do we need these kind of problems in business? O.o

- 2bornot2b

But now it seems like a game

- anonymous

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

- 2bornot2b

Say I have 10 equations and each equations have 10 unknown, how are you going to solve it?

- 2bornot2b

so after having done all these things, I mean whatever you are studying, you will be able to solve linear equations without any effort.

- angela210793

i know wht transposed matrix is....i didn't know why u changed x with y and why not x with z for example

- angela210793

crammer's rule :D

- 2bornot2b

But how did crammer invent that? This is all behind the scenes

- angela210793

i think all these things r unnecessary.....

- angela210793

I'm going to do my hws now...hopefully i'll solve them :) thnx a lot :)

- anonymous

hurmm... sorry can u show me example of that in cramers rule?

- 2bornot2b

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.

- anonymous

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?

- angela210793

this is how I've been taught cramer's rule |dw:1329576915751:dw|

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