angela210793
  • angela210793
Is there anyone who can explain me the range of a matrix???
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
sasogeek
  • 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
  • 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
  • 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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2bornot2b
  • 2bornot2b
Oh! that thing, I am afraid you will have to figure that out yourself.
2bornot2b
  • 2bornot2b
But the key is to practice more and more reduction..
angela210793
  • angela210793
myself????? :O I've tried to...but i don't get it :((((
2bornot2b
  • 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
  • angela210793
ok....can u explain me how u solve aproblem like this in twiddla??
2bornot2b
  • 2bornot2b
Why not here..?
2bornot2b
  • 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
  • angela210793
yea ok ....
2bornot2b
  • 2bornot2b
So will I post an example? Or you will post yours
angela210793
  • angela210793
I'll post one |dw:1329561659776:dw|
2bornot2b
  • 2bornot2b
OK, now tell me what do you feel you must first do, and why?
angela210793
  • angela210793
I have no idea at all :(((
2bornot2b
  • 2bornot2b
OK, now you have to reduce it to something like |dw:1329561739686:dw|
2bornot2b
  • 2bornot2b
With zeros in all the empty spaces, right?
angela210793
  • angela210793
yea tht's smth i know...
2bornot2b
  • 2bornot2b
So start by making the top left corner 1
2bornot2b
  • 2bornot2b
You can do that by two methods, 1. Bring the lowest row to the top, 2. Divide the first column by 3
2bornot2b
  • 2bornot2b
The first method seems easy
2bornot2b
  • 2bornot2b
I just exchanged row 1, and row 3
angela210793
  • angela210793
now u have to make 4 in the 3rd row 1 right?
2bornot2b
  • 2bornot2b
Oh no, there is another, just let me write it fresh...
sasogeek
  • sasogeek
what happened to the 2 at the right corner?
angela210793
  • angela210793
|dw:1329562219705:dw|
2bornot2b
  • 2bornot2b
|dw:1329562156101:dw|
2bornot2b
  • 2bornot2b
Right!
2bornot2b
  • 2bornot2b
Now again think, to make this new matrix similar to |dw:1329562260442:dw|
2bornot2b
  • 2bornot2b
.....you need to make the first element in the 2nd row zero.
angela210793
  • angela210793
i think u'll get a |dw:1329562374039:dw| won't you???
2bornot2b
  • 2bornot2b
i.e. the circled element |dw:1329562329966:dw|
2bornot2b
  • 2bornot2b
Sorry, you lost me.. but did you understand what I meant?
angela210793
  • angela210793
yea yea i understood xD just tell me smth u make a diagonal =1 first and then 0 the other elements??
2bornot2b
  • 2bornot2b
Right!
2bornot2b
  • 2bornot2b
So the next step would be to subtract 2 times row-1 from row-2. Could you follow me?
2bornot2b
  • 2bornot2b
I mean do you feel why I am doing that?
angela210793
  • angela210793
no.....don't u have to make the 4 in the third row 0 first???? O.o
2bornot2b
  • 2bornot2b
Which one? Can you circle it for me?
angela210793
  • angela210793
|dw:1329562705396:dw|
2bornot2b
  • 2bornot2b
No, not at all. All you need to do is keep in mind the picture I gave you and proceed accordingly
2bornot2b
  • 2bornot2b
By picture I meant, the matrix with 1 on the diagonals and 0s elsewhere.
angela210793
  • 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
  • 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
  • 2bornot2b
I mean after reduction your picture will look something like that funny picture.
angela210793
  • angela210793
ahhhhhhhhhhhhhhhaaaaaaaaaaaaaaa......I'm sorry then :/ keep going....why would u multiply first row with 2 and then subtract it to row 2
2bornot2b
  • 2bornot2b
Just to make it look like that funny picture...
2bornot2b
  • 2bornot2b
You will end up with something like |dw:1329563098194:dw|
angela210793
  • angela210793
tht's wht i meant by this pic |dw:1329563199692:dw|
2bornot2b
  • 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
  • 2bornot2b
I really don't understand that notation of yours, but do you understand mine?
2bornot2b
  • 2bornot2b
;)
angela210793
  • angela210793
hahhaha...yea yea xD
2bornot2b
  • 2bornot2b
So just tell me, do you feel why I want to make the element just below 1, zero?
sasogeek
  • sasogeek
sorry to barge in but is it just any diagonal or just the diagonal that cuts through starting with the first number?
sasogeek
  • sasogeek
i mean the diagonal that must be all 1's....
2bornot2b
  • 2bornot2b
Any diagonal...
angela210793
  • 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
  • 2bornot2b
Well, I never learnt it that way...:)
2bornot2b
  • 2bornot2b
May be that is some other method.
angela210793
  • angela210793
ahhhhaaaaaaaaaa...ok then...u do wht u know...:)
sasogeek
  • sasogeek
math is a very clumsy road, u end up at the same destination
angela210793
  • angela210793
i wasn't ending up anywhere with this problem :P
sasogeek
  • sasogeek
did u read the manual/instruction/algorithm to solving this problem?
2bornot2b
  • 2bornot2b
|dw:1329563439879:dw|
2bornot2b
  • 2bornot2b
Is that clear?
angela210793
  • angela210793
wht did u do in there?????
angela210793
  • angela210793
OMG!!! I'm hopeless x( :(:(
2bornot2b
  • 2bornot2b
R2-2R1
2bornot2b
  • 2bornot2b
got it or not?
angela210793
  • angela210793
wasn't the first element of the 2nd row supposed to b zero??? 2-(2*1)=2-2=0
2bornot2b
  • 2bornot2b
Oh, does that thing look like 6, its actually 0..
2bornot2b
  • 2bornot2b
lol
angela210793
  • angela210793
ahhhhaaaaa...ok then xD
2bornot2b
  • 2bornot2b
Next you need to turn the first element in the third row equal to zero
angela210793
  • angela210793
would tht be R3-3R1???
sasogeek
  • sasogeek
wait so u do 1 0 0 column by column, as in one column after the other?
2bornot2b
  • 2bornot2b
|dw:1329563860051:dw|
2bornot2b
  • 2bornot2b
Sasogeek is right!
sasogeek
  • sasogeek
1000 0100 0010 u should end up with this... right?
2bornot2b
  • 2bornot2b
Exactly, but it may look a little different, but something similar to that.. P.S. angela210793 you typed the right notation
angela210793
  • angela210793
ok....no now u have to make -3 in the 2nd column zero...how do u do tht???
2bornot2b
  • 2bornot2b
First of all, can you check, if I did the calculations correct?
angela210793
  • angela210793
hang on
angela210793
  • angela210793
|dw:1329564323164:dw|
2bornot2b
  • 2bornot2b
Thats right! I think
angela210793
  • angela210793
i think so too O.o.....wht's next?
2bornot2b
  • 2bornot2b
So the matrix which we now have is |dw:1329564404847:dw|
2bornot2b
  • 2bornot2b
Now this particular problem was prepared in such a way, that we ended up with the 2nd and third row as equal
2bornot2b
  • 2bornot2b
But that is a nice case, it will not happen always.
2bornot2b
  • 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
  • 2bornot2b
Once the circle element is made 1, you will attempt to make all the elements below it equal to 0
angela210793
  • angela210793
can we multiply the second row with 1/7???
2bornot2b
  • 2bornot2b
Yes, that is exactly what you should have done if you were a computer.
anonymous
  • anonymous
can.. but it would be complicated
anonymous
  • anonymous
try avoiding fractions form..
angela210793
  • angela210793
then what?? O.o
2bornot2b
  • 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
  • 2bornot2b
And that will make the whole of third row equal to zero
angela210793
  • angela210793
ohhhhhh...well i'm not a random person...I think like a computer :P
2bornot2b
  • 2bornot2b
|dw:1329564788814:dw|
angela210793
  • angela210793
7 is still 7...wht now?
2bornot2b
  • 2bornot2b
So now clearly you have two non zero rows, you can now say, that the range is 2
anonymous
  • anonymous
R3=R3+R2
angela210793
  • angela210793
:O wht??? how was tht ..can u explain me once again please ???
anonymous
  • anonymous
ops it is R3=R3-R2
2bornot2b
  • 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
  • angela210793
Hmmmmmmmmmmmm......ok.... Thank u very much :))))))))))) all of u, especially 2bornot2b :)) Gosh...How can u b so patient????
anonymous
  • anonymous
i dont understand what is range?
2bornot2b
  • 2bornot2b
Here is a good problem
angela210793
  • angela210793
i don't think it is good :P
2bornot2b
  • 2bornot2b
I meant it gives you the feel of what you need to do in real problems
anonymous
  • anonymous
ok now i understad what is range.. :)
2bornot2b
  • 2bornot2b
And you can see in the reduction, things go in the same algorithm as I mentioned
anonymous
  • anonymous
so for the attachement given.. the range is 3 right?
2bornot2b
  • 2bornot2b
Right xilem
anonymous
  • anonymous
ok now i understand.. but what it is for?
2bornot2b
  • 2bornot2b
Something very deep xilem, its for actually solving linear equation.
angela210793
  • angela210793
yea...why do we need these kind of problems in business? O.o
2bornot2b
  • 2bornot2b
But now it seems like a game
anonymous
  • 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
  • 2bornot2b
Say I have 10 equations and each equations have 10 unknown, how are you going to solve it?
2bornot2b
  • 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
  • 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
  • angela210793
crammer's rule :D
2bornot2b
  • 2bornot2b
But how did crammer invent that? This is all behind the scenes
angela210793
  • angela210793
i think all these things r unnecessary.....
angela210793
  • angela210793
I'm going to do my hws now...hopefully i'll solve them :) thnx a lot :)
anonymous
  • anonymous
hurmm... sorry can u show me example of that in cramers rule?
2bornot2b
  • 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
  • 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
  • angela210793
this is how I've been taught cramer's rule |dw:1329576915751:dw|

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