For about 3 days now I’ve been absolutely stumped by solving equations with the gauss Jordan method and finding the inverse of 3x3 matrices, I understand that you are meant to solve the top right to one first but how to get there correctly without messing up the answer has brought so much frustration. If anyone could help tutor me or just help me out in general in teaching the proper way to do so it would be appreciated a ton.
#Im having major struggles with solving 3x3 Gauss Jordan matrices and inverse matrices
elder yacht
civic robinBOT
elder yacht
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pearl chasm
can you send a practice problem of one you are trying to do and the steps you do to solve it
elder yacht
ofc!
Like this one (though it’s unfinished as it’s my 4th go through on it) where there are multiple ways to single out that one in a11
Im just stumped because all those different ways result in varying answers that result in other varying answers and I’m just so confused at this point 😞
pearl chasm
so you are tryign to get the inverse of the matrix by adjoining it to the identity matrix right
elder yacht
Yup!
pearl chasm
sorry was doing something
elder yacht
its alright
pearl chasm
so remember our goal is to get the identity matrix to be on the left matrix by the end as that will mark the end of our steps and show that we have gotten the inverse matrix
elder yacht
yeah I understand that loosely its just the getting there is what ive been stumped on
pearl chasm
ok so lets start from the beginning after adjoining it
lets try to get row 1 col 1 to turn into 1
any ideas on what step we should do to make that happen ?
elder yacht
subtracting r1 by r2?
ripe stag
so you are tryign to get the inverse of the matrix by adjoining it to the identi...
(side note why not cofactors)
pearl chasm
(side note why not cofactors)
thats for determinants
pearl chasm
subtracting r1 by r2?
close, we would add r2 to r1
so R1 + R2
since r2 starts with -1 we will get 2 + -1 which will make our first column turn into 1
ripe stag
transpose of matrix of cofactors over det is inverse but thats way too impractical
elder yacht
since r2 starts with -1 we will get 2 + -1 which will make our first column turn...
gotcha!
ripe stag
but yeah you can uh
r1+r2 -> r1
elder yacht
transpose of matrix of cofactors over det is inverse but thats way too impractic...
wuh??????😭
ripe stag
now what do you do with that to get 1st row 2nd column as 0
pearl chasm
wuh??????😭
dont worry youll be doing that later in like 3 months
elder yacht
dont worry youll be doing that later in like 3 months
im gonna go crazy i swear
ok ok
pearl chasm
oh wait i noticed something that i didnt at the beginning so remember we want it to end with 1 0 0 , 0 1 0 , 0 0 1 so we want our bottom row to have a 1 at the end so we should swap something
which one would you like to swap ?
pearl chasm
yeah that works
elder yacht
it wouldnt mess up the end result?
pearl chasm
actually no that wouldnt work because our first row needs to start with a 1 also
elder yacht
ahh i see okay okay
pearl chasm
so which one do you think we should wap if the first row and third row swap isn't valid ?
elder yacht
ahh okay okay row 1 with row 2 to get -1 on top
pearl chasm
that also works, but it doesnt help the fact that row 3 is missing a number in row 3 col 3
remember for us to get the identity matrix there should be a number in the green spots so we should do a swap so the green diagonal has numbers in it
it will help us stay focuesd on the goal
elder yacht
ahh i see i see so our goals at first should be to ensure that there is a number that isnt 0 so that we can get them into 1s later?
pearl chasm
exactly
elder yacht
so is that for every single one of these problems as well? ensure that there is a number in each of those dots
pearl chasm
you can do it for every single problem and it will help its just what i like to do not sure if is the most efficent but it hasnt failed me yet
elder yacht
I see okay okay so
swap R2 and R3 so that there is a number other than 0 in those circles first
pearl chasm
also i had a slight mistake in my adjoining matrix i fixed here because i forgot to swap that side
pearl chasm
look at the picture i sent earlier i for got to swap the adjoined matrix when i swapped row 2 and row 3
so i fixed it in that image
pearl chasm
so after that we get R11 to a 1 then R21 to a 0 after
wdym by this
elder yacht
mb by R11 i mean like row 1 collumn 1 and R21 I mean Row 2 collumn 1
pearl chasm
oh in that case yes that should be our goal
i like to get row 1 col 1 to be 1 first and work my way down into making the diagonal into 1s staring from the top
so first lets try to get a 1 in row 1 col 1. Do you have any ideas on what we should do to get that ?
elder yacht
adding R3 to R1
elder yacht
alright! gimme a sec ill also do some more steps after then lmk on what you think
pearl chasm
elder yacht
ok ok
pearl chasm
all you did was good until the 5th matrix
remember you want the identity matrix on the left side
so what i would have done is multiply row 2 by 3 and add it to row 3
the bottom matrix is where i did what i suggested
elder yacht
but arent you meant to get rid of the negatives first?
pearl chasm
no it doesnt make a difference whether you get rid of them first or at the end
instead you should use them to your advatage to cancel things out like i did
because it doesnt matter if i make the negative postive now or if i do it at the end i will end up with the same result either way
elder yacht
I see so as long as you can get it to a 1 or -1 either one will work no matter what as well?
pearl chasm
yes, just remember to make it postive once you are completely done
which is as simple as just multiplying the whole row by (-1)
elder yacht
I see let me fix it now and ill update you in a sec
pearl chasm
elder yacht
ok ok sorry it took a second got busy with something in between
pearl chasm
its ok dont worry im waiting on a friend to play a game with anyways so i got nothing to do
but he has not gotten off the game hes been on for the past 7 hours 🙏 😭
wait bro is a joe bart viewer
elder yacht
wait bro is a joe bart viewer
yuh
Ok so here’s what I did though I think I went wrong somewhere
pearl chasm
🫡
elder yacht
ahh i see what i did wrong now nvm 1 sec
pearl chasm
yup i see it
you accidentally forgot to put a 1 in row 1 col 2 and put a 0 which led you slightly off
besides that everything is right so once you fix that you should get the right answer
elder yacht
yeah but thankfully it doesnt take awfully long to fix
YAY
I DID IRT
YIPEE
horray
elder yacht
pearl chasm
if you ever need help with linear algebra, and or calculus feel free to send me a message if im free ill help