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UsukiDoll
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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
UsukiDoll Group Title
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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UsukiDoll Group TitleBest 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

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anywaydw:1361067211535:dw
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UsukiDoll Group TitleBest ResponseYou've already chosen the best response.0
I'm using elementary row operations.
 one year ago

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spotted anotehr error. not my day today
 one year ago

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dw:1361067436003:dw
 one year ago

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arghhh...
 one year ago

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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

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

Callisto Group TitleBest 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

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

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ok let's redo this
 one year ago

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dw:1361067604121:dw
 one year ago

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augmented matrix [a b]
 one year ago

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dw:1361067630686:dw triangles indicate main diagonal
 one year ago

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so I have to get rid of the 4 and the 3.
 one year ago

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2row 1  row 2 > row2
 one year ago

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

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
do you mean \[R_2\to R_22R_1\] @UsukiDoll
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dw:1361067762579:dw
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 one year ago

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so now... to get rid of the 3... 7row1 3row2 >row1
 one year ago

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

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achhhhhhhhhhhh
 one year ago

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I don't wanna deal with fractions
 one year ago

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

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dw:1361067930957:dw
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UsukiDoll Group TitleBest ResponseYou've already chosen the best response.0
arghhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh I feel like Rarity Belle now
 one year ago

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dw:1361067978329:dw
 one year ago

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oh wait. sign errors everywhere. Is that why I am getting frustrateD?
 one year ago

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wait a sec something is wrong already with row 2
 one year ago

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

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dw:1361068165204:dw
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argh there could be so many combinations with this thing!
 one year ago

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

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arghhhhhhhhhhhhh doing that got me x = 7
 one year ago

Callisto Group TitleBest 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

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big numbers _
 one year ago

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that means to get rid of the 6 I have to do 7r1  6r2
 one year ago

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or 7r1+6r2
 one year ago

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dw:1361068464895:dw
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dw:1361068472375:dw main diagonal in triangles
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Callisto Group TitleBest ResponseYou've already chosen the best response.3
Yup..Do you want to deal with big numbers or fractions?
 one year ago

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dw:1361068571208:dw
 one year ago

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I don't want to deal with fractions
 one year ago

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 one year ago

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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

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

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

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

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

UsukiDoll Group TitleBest 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

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

Callisto Group TitleBest 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

UsukiDoll Group TitleBest ResponseYou've already chosen the best response.0
I had a truckload
 one year ago

UnkleRhaukus Group TitleBest 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

Callisto Group TitleBest 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

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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

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Gauss Jordan is worse than Gaussian
 one year ago

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ohhhhh what happens if I did Gaussian and then Gauss Jordon
 one year ago

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because the answers to the Gaussian are supposed to be the same as the Gauss Jordon
 one year ago

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Gaussian Jordan = Gaussian then Jordan lol!!!
 one year ago

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but sometimes when I put the matrix into echleon form I can see the steps to making it row reduced
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dw:1361069849783:dw
 one year ago

Callisto Group TitleBest 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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*Gaussian
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____________________ 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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Just a minute..
 one year ago

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dw:1361070023727:dw
 one year ago

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uighhhhhhhhhhhhhhhh mind blown
 one year ago

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Gaussian and then Gaussian Jordan yeahhhhh
 one year ago

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I found the x = 1/7 just doing the Gaussian
 one year ago

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dw:1361070037568:dw
 one year ago

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yeahhhh...now I really should've done Gaussian first and then the Jordan version
 one year ago

Callisto Group TitleBest 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

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dang that means I have to redo some practice problems...gawd not again wasting paper here.
 one year ago

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oh yeah now I got it
 one year ago

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yup works. I went way too ahead... x.x
 one year ago

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so now I gotta correct all of these problems and write a proof...nice X___X
 one year ago

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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