#Augmenting matrices techniques

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queen flower
midnight agateBOT
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queen flower
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I genuinely have no idea what to do to solve this system of equations

urban hedge
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@queen flower how would you solve let's say a simpler system

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Like 2x+3y=1
3x+2y=1

slender socket
lost voidBOT
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@queen flower

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lost voidBOT
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@slender socket @urban hedge The user still needs help with this help request.

queen flower
urban hedge
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Back after so long

queen flower
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I was travelling

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Rushing myself mb

urban hedge
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Aren't we all travelling

queen flower
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Is your pfp from chainsaw man

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Anyways

queen flower
urban hedge
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Yeah

queen flower
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Same process?

urban hedge
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That's basically how rref works

queen flower
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Rref?

urban hedge
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Try to get top most entries that haven't been made 1 yet

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Eliminate everything below

queen flower
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Okok

urban hedge
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Should I draw u a picture?

queen flower
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No get the top left to be 1 then middle left to be 0 then bottom left to be 0

urban hedge
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Yes

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The repeat with the bottom equation

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And so on

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Basically

queen flower
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So bottom right to be 1

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And everything on top to be 0

urban hedge
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Find the left most upper non zero entry

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Make it one by multiplication or division by appropriate scalr

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Use it to eliminate any coefficients below it

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Rinse and repeat with the below rows

queen flower
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Ok

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I think

urban hedge
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So forthis

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First divide the equation 1 by 2

queen flower
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Yes okay

urban hedge
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Eliminate everything below

queen flower
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I thought we avoid fractions

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Nvm

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Ok

slender socket
slender socket
urban hedge
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It always works

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And nothing wrong with fractions

slender socket
queen flower
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My mental maths is what is wrong with fractions

slender socket
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I prefer using Gauss's method in such a way that avoids fractions until the very end.

urban hedge
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It's 3 equations and 3 variables

queen flower
urban hedge
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I mean what matters is solving them

slender socket
urban hedge
queen flower
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With the augmented matrices?

slender socket
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You know, the one where you use row operations to bring the matrix to the RREF (or a REF).

urban hedge
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Bro

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It's the same shit

slender socket
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Ok, fine. Do what you want.

urban hedge
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Yeah

queen flower
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Nah wait

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If avoiding fractions is more preferable

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Why wouldn’t I go for that

urban hedge
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And what would happen if your coefficients were in reals

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Still would be able to avoid fractions

slender socket
urban hedge
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Yes it is lmao

queen flower
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What is realms

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Reals*

urban hedge
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It's shit getting too real

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Anyways

queen flower
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I got a question anyway

urban hedge
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If darpy is willing to help you with a better shitill leave itto him

slender socket
queen flower
queen flower
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What’s after this step

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Bottom equation?

slender socket
urban hedge
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Take 16 out

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I mean divide by 16

queen flower
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And make it 1?

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Ok

urban hedge
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And then eliminate the coefficients above and below

queen flower
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Ok

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Wait how

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Idk how to without changing the one 1 i alr have in my upper left

urban hedge
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The below is a 0

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The number below 1 is 0

queen flower
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Yes

urban hedge
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It adding the second row to above and below won't affect the first column

queen flower
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What

urban hedge
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You know what let me do it for you?

queen flower
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Yh

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I haven’t had an example with three unknowns yet

urban hedge
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Eliminate the below likewise

queen flower
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Ohhh Yh

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Cause it’s 0

urban hedge
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Yeah

queen flower
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There was too many fractions

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I gave up

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@slender socket

slender socket
# queen flower

So, my approach involves making as many small integers as possible.
Here we don't have any leading 1s, but we can make a couple by doing II - 2I, III - I.

queen flower
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Okay hold on

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Which row do I apply them to

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Of the II-2I on the second row

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And the other on the third?

slender socket
queen flower
slender socket
# queen flower

You might want to write that six at the top a bit better...

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It really looks like a zero.

queen flower
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It is a 0

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My bad I’m falling asleep here

slender socket
queen flower
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The second matrix is after I did the augmentation

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You suggested

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And then divide by 3?

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For first row

slender socket
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No, wait.

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Oh, actually, you're right! We could've started with I*(1/3).

urban hedge
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Well whatever suits you

lost voidBOT
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@queen flower

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queen flower
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+close

lost voidBOT
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lost voidBOT
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