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|dw:1361067093589:dw|

|dw:1361067118822:dw|

ugh I missed that one on my paper! that subtraction because -16-(-2) is - 14

anyway|dw:1361067211535:dw|

|dw:1361067247174:dw|

|dw:1361067302376:dw|

|dw:1361067336310:dw|

|dw:1361067340708:dw|

|dw:1361067371987:dw|

I'm using elementary row operations.

oh crud

spotted anotehr error. not my day today

|dw:1361067436003:dw|

arghhh...

Hmm... Try to do it again...

Since you've made a mistake in the first operation, it's hard to get the right answer :|

something is wrong with the y

ok let's redo this

|dw:1361067604121:dw|

augmented matrix [a b]

|dw:1361067630686:dw| triangles indicate main diagonal

so I have to get rid of the 4 and the -3.

2row 1 - row 2 --> row2

Hmm.. My usual practice is -2R1 + R2 -> R2

do you mean \[R_2\to R_2-2R_1\] @UsukiDoll

yes

|dw:1361067762579:dw|

|dw:1361067803078:dw|

so now... to get rid of the -3... 7row1 -3row2 --->row1

Why not do this: -1/7 R2 -> R2

achhhhhhhhhhhh

I don't wanna deal with fractions

But the answers are fractions :P

|dw:1361067930957:dw|

arghhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh I feel like Rarity Belle now

|dw:1361067978329:dw|

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

wait a sec something is wrong already with row 2

|dw:1361068119755:dw|

|dw:1361068152547:dw|

Relax~~~
|dw:1361068054013:dw|

|dw:1361068165204:dw|

argh there could be so many combinations with this thing!

|dw:1361068179917:dw|

|dw:1361068217096:dw|

|dw:1361068228254:dw|

Just stop for a while, if you don't mind?

arghhhhhhhhhhhhh doing that got me x = 7

big numbers -_-

that means to get rid of the 6 I have to do 7r1 - 6r2

No?!

or -7r1+6r2

-.-

|dw:1361068464895:dw|

|dw:1361068472375:dw| main diagonal in triangles

|dw:1361068495592:dw|

|dw:1361068548208:dw|

Yup..Do you want to deal with big numbers or fractions?

|dw:1361068571208:dw|

I don't want to deal with fractions

|dw:1361068639980:dw|

Yes!!!

|dw:1361068650303:dw|

|dw:1361068693152:dw|

just earlier I got x = -1 and y = -2

Hmm.. Careless mistakes perhaps?!

now x = 1/7 y = -18/7

what!

The one x=1/7; y=-18/7 is right :\

No.

x = 1/7
y = -18/7 \(\LARGE\checkmark\)

I had a truckload

Gauss Jordan is worse than Gaussian

ohhhhh what happens if I did Gaussian and then Gauss Jordon

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

Gaussian Jordan = Gaussian then Jordan lol!!!

but sometimes when I put the matrix into echleon form I can see the steps to making it row reduced

|dw:1361069849783:dw|

*Gaussian

|dw:1361069869054:dw|

|dw:1361069916982:dw|

|dw:1361070002077:dw|

Just a minute..

|dw:1361070023727:dw|

uighhhhhhhhhhhhhhhh mind blown

Gaussian and then Gaussian Jordan yeahhhhh

I found the x = 1/7 just doing the Gaussian

|dw:1361070037568:dw|

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

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

oh yeah now I got it

yup works. I went way too ahead... x.x

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

Are you doing high school maths or college maths?

college math

Proofs of??

umm should I type it?

I.. didn't know what was a proof :S Please type it, if you don't mind!

*that instead of what

It also has something to do with the homogenous system as well.

If a matrix is nonsingular, an inverse exists...so Theorem 2.9 doesn't work at all

oh yeah this is just a rough draft of it

I know. What if we let A be the inverse of B?

that would be Matrix B
A = B^-1
BB^-1 = identity matrix

What if \(A \ne B^{-1}\) and \(B \ne A^{-1}\) ?

I think that the only way that occurs is if A and B are singular

*contradiction, * neither A nor B can be singular

omg how did u get that so fast?

I haven't learned determinants yet. That's chapter 3 in my book

What if I'm forced to use that Theorem? then what?

but can we use that if AB is non-singular, then |AB| not =0
....grrrr, i guess not ..

nnooo...

using advanced things aren't allowed otherwise my prof will get suspicious.

he was like DON'T USE ANYTHING THAT WASN'T INTRODUCED!!!!!!!!! IT'S A BAD IDEA

ok ok wait....

What if B =/= inverse of A?

what if B isn't the inverse of A?

:/

so many contradictions everywhere. That's all I can get out of this thing.

nontrivial solution in a homogenous system is NOT a 0, so how the heck can Ax =0?

I gotta go...bye... x__X

just last small try.

^ actually it does. thanks :D