Hi just need some help remembering the steps for a 3x3
#finding the inverse of a 3x3 matrix
spice veldt
austere valveBOT
Hi just need some help remembering the steps for a 3x3
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spice veldt
A matrix is invertible if and only if the determinat is not 0
The determinat can easily be computed: 1 * det( 1 9 | 0 1 ) = 1 - 0 = 1
So it is invertible
I forgot the rest 
spice veldt
I forgot the rest <:clown_skull:1003667024553201667>
ðŸ˜ðŸ˜ðŸ˜lmfao
rose raptor
ðŸ˜ðŸ˜ðŸ˜lmfao
To find A^-1 you can use Gaussian operations to reduce your matrice to the identity matrice
Then do the same operations on the identity matrice
You’ll get it’s inverse
Like if AX=I here X=A^-1 then P * A *X=P thus X=P with P the matrice representing the product of all Gaussian operations matrices
That or find the comatrix of A transpose it and you’ll get the inverse, this is an orthogonal matrice so it’s inverse is the transpose of the comatrix
spice veldt
Like if AX=I here X=A^-1 then P * A *X=P thus X=P with P the matrice representin...
What are the Gaussian operations?
rose raptor
Hmm well here you want to reduce your matrice to the identity matrice
So take the last line and subtract it 9 time too the second line
And add the last line once to the first line
You’re matrice will be then [1,4,0;0,1,0;0,0,1]
Last step is too subtract the second line 4 times to the first line
When you do that your matrice is reduced to the identity
Now to get the inverse you need to repeat these exact operations on the identity matrice
rose raptor
What are the Gaussian operations?
I Hope this isn’t too confusing
hazy coral
isnt it easier to do if u use the normal formula where A^-1 = adjoint(A)/|A|
since the determinant of the matrix is 1, simply find the adjoint of A
rose raptor
isnt it easier to do if u use the normal formula where A^-1 = adjoint(A)/|A|
Idk for me just applying the operations 3 times is faster
Btw does comatrix and adjoint matrix represent the same thing?
hazy coral
ive never heard of a comatrix
hazy coral
Idk for me just applying the operations 3 times is faster
probably i dont know about that method, i just do it by finding the adjoint
rose raptor
It’s the transpose of the cofactor matrice right ?
hazy coral
yes
rose raptor
Okaaay in my country we refer to it as comatrix
hazy coral
ahh
hazy coral
if its a 2x2, adjoint is prob faster
spice veldt
isnt it easier to do if u use the normal formula where A^-1 = adjoint(A)/|A|
Okay yes that’s what I’m supposed to do
spice veldt
Okaaay in my country we refer to it as comatrix
I was so confused by thisðŸ˜ðŸ˜ okay yea that makes sense
Thank you guys sm