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solve the system of linear equations
using the Gauss–Jordan elimination method.
2x3y=8
4x+y=2
 one year ago
 one year ago
solve the system of linear equations using the Gauss–Jordan elimination method. 2x3y=8 4x+y=2
 one year ago
 one year ago

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UsukiDollBest ResponseYou've already chosen the best response.0
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UsukiDollBest ResponseYou've already chosen the best response.0
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 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
ugh I missed that one on my paper! that subtraction because 16(2) is  14
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
anywaydw:1361067211535:dw
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
dw:1361067247174:dw
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UsukiDollBest ResponseYou've already chosen the best response.0
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CallistoBest ResponseYou've already chosen the best response.3
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UsukiDollBest ResponseYou've already chosen the best response.0
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CallistoBest ResponseYou've already chosen the best response.3
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UsukiDollBest ResponseYou've already chosen the best response.0
I'm using elementary row operations.
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
spotted anotehr error. not my day today
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
dw:1361067436003:dw
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
ok really...I put this in reduced row echleon form. got my solution, but geez doesn't even equal back into the equation
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Hmm... Try to do it again...
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Since you've made a mistake in the first operation, it's hard to get the right answer :
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
something is wrong with the y
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
dw:1361067604121:dw
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
augmented matrix [a b]
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
dw:1361067630686:dw triangles indicate main diagonal
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
so I have to get rid of the 4 and the 3.
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
2row 1  row 2 > row2
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Hmm.. My usual practice is 2R1 + R2 > R2
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
do you mean \[R_2\to R_22R_1\] @UsukiDoll
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
dw:1361067762579:dw
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UsukiDollBest ResponseYou've already chosen the best response.0
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 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
so now... to get rid of the 3... 7row1 3row2 >row1
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Why not do this: 1/7 R2 > R2
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
I don't wanna deal with fractions
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
But the answers are fractions :P
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
dw:1361067930957:dw
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
arghhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh I feel like Rarity Belle now
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
dw:1361067978329:dw
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
oh wait. sign errors everywhere. Is that why I am getting frustrateD?
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
wait a sec something is wrong already with row 2
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dw:1361068119755:dw
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UsukiDollBest ResponseYou've already chosen the best response.0
dw:1361068152547:dw
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Relax~~~ dw:1361068054013:dw
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
dw:1361068165204:dw
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
argh there could be so many combinations with this thing!
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
dw:1361068179917:dw
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UsukiDollBest ResponseYou've already chosen the best response.0
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UsukiDollBest ResponseYou've already chosen the best response.0
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 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Just stop for a while, if you don't mind?
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
arghhhhhhhhhhhhh doing that got me x = 7
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
This is basically what you do for the first row operation 2R1 + R2 > R2. I split it into two steps so that you can catch up the the arithmetic easier (I hope..) dw:1361068290374:dw
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
that means to get rid of the 6 I have to do 7r1  6r2
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
dw:1361068464895:dw
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
dw:1361068472375:dw main diagonal in triangles
 one year ago

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dw:1361068495592:dw
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UsukiDollBest ResponseYou've already chosen the best response.0
dw:1361068548208:dw
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Yup..Do you want to deal with big numbers or fractions?
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
dw:1361068571208:dw
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
I don't want to deal with fractions
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
dw:1361068639980:dw
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UsukiDollBest ResponseYou've already chosen the best response.0
dw:1361068650303:dw
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UsukiDollBest ResponseYou've already chosen the best response.0
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 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
ok why the heck am I getting different answers despite the fact that I got it into reduced row echleon form. that's just...grrrrrrrrrrrrrrrrrr
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
just earlier I got x = 1 and y = 2
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Hmm.. Careless mistakes perhaps?!
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
now x = 1/7 y = 18/7
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
The one x=1/7; y=18/7 is right :\
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
. is there more than one answer to this? There could be many many things that I could have done here.
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
x = 1/7 y = 18/7 \(\LARGE\checkmark\)
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
There are only 3 cases for system of linear equations.. 1. No solution 2. Exactly one solution 3. Infinitely many solution.
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
A quick string of row operations \[R_2\to R_22R_1\\R_2\to R_2/7\\ R_1\to R_1+3R_2\\R_1\to R_1/2\], if you have gotten a different solution you must have a made a mistake somewhere, it is very easy to make mistakes using Gauss–Jordan elimination .
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
1. No solution with a row that has all zero entries on the left, but nonzero entry on right => system is inconsistent 2. Exactly one solution After elementary row operations, no. of rows = no. of unknowns (/columns) => system is consistent 3. Infinitely many solution. After elementary row operations, no. of rows < no. of unknowns => system is consistent
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
but...yeah I suppose because I have seen some matrices that had a row of zeros on the left but with a nonzero on the right that is an inconsistent system .. How is it possible to make a mistake when it's so hard to spot one? I mean...I could've used different operations on the matrix. The combinations are everywhere.
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
Gauss Jordan is worse than Gaussian
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
ohhhhh what happens if I did Gaussian and then Gauss Jordon
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
because the answers to the Gaussian are supposed to be the same as the Gauss Jordon
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Gaussian Jordan = Gaussian then Jordan lol!!!
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
but sometimes when I put the matrix into echleon form I can see the steps to making it row reduced
 one year ago

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dw:1361069849783:dw
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Guassian told you to make the left an upper triangular matrix Jordan asked you to further make the left an identity matrix
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UsukiDollBest ResponseYou've already chosen the best response.0
dw:1361069869054:dw
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dw:1361069916982:dw
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UsukiDollBest ResponseYou've already chosen the best response.0
____________________ this is just Gaussian... WHAT THEEEEE!!!!!!! I see y = 18/7 oh I haven't solved yet oops
 one year ago

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dw:1361070002077:dw
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dw:1361070023727:dw
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UsukiDollBest ResponseYou've already chosen the best response.0
uighhhhhhhhhhhhhhhh mind blown
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
Gaussian and then Gaussian Jordan yeahhhhh
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
I found the x = 1/7 just doing the Gaussian
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
dw:1361070037568:dw
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
yeahhhh...now I really should've done Gaussian first and then the Jordan version
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Gaussian > Make the left an upper triangular matrix Jordan > Make the left an identity matrix GaussianJordan => Make it an upper triangular matrix, then further make it an identity matrix. That's what GaussanJordan is! Jordon helps you to get the answer by matching the left and the right That is for the row [1 0  1/7], you can tell immediately that x = 1/7 It's just the same as doing Gaussian elimination then back substitution.
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
dang that means I have to redo some practice problems...gawd not again wasting paper here.
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
oh yeah now I got it
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
yup works. I went way too ahead... x.x
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
so now I gotta correct all of these problems and write a proof...nice X___X
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
Callisto do you know how to write proofs? I got a partial first draft and I was wondering if you could critique it?
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Are you doing high school maths or college maths?
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
like the one I am currently writing is a contradiction proof. contradicts a theorem at least 23 times
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
umm should I type it?
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
I.. didn't know what was a proof :S Please type it, if you don't mind!
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
*that instead of what
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
okkk... Let A and B be n x n matrices. Show that if AB is nonsingular then A and B must be nonsingular.(Hint Use Theorem 2.9) Theorem 2.9 states that the homogeneous system of n linear equations in n unknowns Ax = 0 has a nontrivial solution if and only if A is singular.
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
There's a contradiction....namely because if Matrix A is singular, then the inverse of Matrix A does NOT exist which means that AB doesn't exist as well.
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
It also has something to do with the homogenous system as well.
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
because basically a homogeneous system is always consistent. However, a homogeneous system's solution is always 0 and it's a trivial solution. Nontrivial solution in a homogenous system means that the solution IS NOT 0 at all!
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
so, what is given before proving is that A and B are n x n matrices A and B must be nonsingular AB is also nonsingular Theorem 2.9
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
If a matrix is nonsingular, an inverse exists...so Theorem 2.9 doesn't work at all
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Forgive me, I don't understand the part "... which means that AB doesn't exist as well" I understand if A is singular, A^(1) doesn't exist, but not the which means part..
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
oh yeah this is just a rough draft of it
 one year ago

UsukiDollBest ResponseYou've already chosen the best response.0
hmm if A is nonsingular, an inverse exists. I remember back from Theorem 1.5 that it was AB=BA=In. B is the inverse of A. hmmm..if A is singular, yes the inverse doesn't exist. Let's have B = the inverse of A. Matrix A is singular Inverse doesn't exist so B doesn't exist AB is impossible to achieve unless A is nonsingular
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Hmm.. \[AA^{1} = A^{1}A=I\]provided that \(A^{1}\) exists...  But what about \(B \ne A^{1}\)? And we also have to show that B is also nonsingular?!
 one year ago

UsukiDollBest Response