Inverse of matrix

[@wolframalpha8634]

The inverted Gauss is telling Dr.Peyam is so cool !!

[@Mecolo]

infinitely clearer than my lessons of linear algebra at my university 👌👌👌👍👍

[@blackpenredpen]

Peyam, the title should be “how to find the inverse of a matrix” or something like that. So it’s searchable

[@PackSciences]

You can also use comatrix and determinant: A^-1 = 1/det(A) * transpose(com(A)) providing det(A) is non-zero.

[@drpeyam]

Of course ;) That’ll be part of a next video. But that’s painful for 4x4 matrices and above

[@PackSciences]

@@drpeyam The secret is to say that you have used comatrix but actually you used wolfram alpha *EVIL LAUGH*

[@guigazalu]

It's so lovely & awesome how things are so organized in these playlists, where even the titles are plain simple, but with the information needed

[@drpeyam]

Thanks so much!!! 😊

[@andreynogueira7419]

How can I leave 2 likes? Absolutely LOVED IT

[@holyshit922]

If you want to write a program in your favourite language you must use partial pivoting Patial pivoting means that you firstly look for max absolute value in column and then swap rows

[@alextrigoso]

I won't forget this !

[@shayanmoosavi9139]

Me from 0:00-5:42 : NANI??!! Me at 6:44 : oooohh. I got it now. Wow it was an amazing way to do it. So no need to calculate the determinant?

[@drpeyam]

Exactly

[@Invalid571]

The pic at the thumbnail should be flipped like facing a mirror. ☺

[@neilgerace355]

Very concise treatment

[@johnjoshua7282]

Thankyou! that was helpful

[@ThinkDifferentlier]

Hello, I would like to ask for a follow up video about the Stieltjes integral. Maybe about a function that is clearly non-Riemann integrable but gives a neat result as Stieltjes integral. Just to show that Stieltjes integral is not a mathematical gimmick but a powerful and useful tool in calculus.

[@soumyachandrakar9100]

You looks like Sal Khan from KhanAcademy!

[@dsfdsfsfdsfdsfd]

Nice video! you can also prove that an invertible matrix is the product of elementary matrices. it's an easy proof but a nice one

[@drpeyam]

That’s part of another video :)

[@faizanurrehman6220]

Nice work👍💕

[@hansisbrucker813]

I really need to go back to learning row echelon form. I'm learning linear algebra on Khan Academy 🤔

[@wolframalpha8634]

Hey Dr.payam!!:D

[@drpeyam]

Hi! 👋

[@wolframalpha8634]

@@drpeyam hii :D :D

[@cameronspalding9792]

When I do row addition I write it separately

[@newtonnewtonnewton1587]

Nice

[@rakhimondal5949]

We can also do it by adj(a)/|a| Right??

[@drpeyam]

Yeah, but that’s bad for 4x4 matrices and higher

[@cameronspalding9792]

For an n*n dimensional matrix The number of steps to compute the inverse is O(n!)

[@ssdd9911]

6:08 what happened

[@drpeyam]

s sdd Lights went off in the room

[@NoNTr1v1aL]

Does AB = I imply that BA = I ?

[@drpeyam]

Only if A is a square matrix

[@NoNTr1v1aL]

@@drpeyam But in general matrix multiplication is noncommutative right? What if BA is not equal to I ?

[@waterfirecards5128]

Mohammed Sharukh yes because matrix multiplication is a transformation and B when defined as AB=I means that B is the opposite transformation of matrix A and that applies that A is the opposite transformation of matrix B which applies that their multiplication is commutative.

[@NoNTr1v1aL]

@@waterfirecards5128 I know the analogy between linear transformations and matrix multiplication from 3b1b. But that doesn't answer my question. If I apply B then A to get I, how do I know for sure that if I reverse the order then I'll get back to I ? Like I said before, matrix multiplication is in general noncommutative, i.e. the order of the transformations matters.

[@willnewman9783]

@@NoNTr1v1aL I got you bro: If AB=I, multiply both sides on the right by B^-1. We see that A=B^-1. Then you can multiply both sides on the right by B to get BA=I

[@japotillor]

RI, who threw potential difference in inverse matrices :p

[@jiyoonpark5022]

RaR