Computing inverse matrices using Gaussian elimination | Lecture 12 | Matrix Algebra for Engineers

How to compute the inverse of a matrix by computing the reduced row echelon form of the matrix.
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Lecture notes at www.math.ust.hk/~machas/matrix...
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[@ProfJeffreyChasnov]

Find other Matrix Algebra videos in my playlist kzbin.info/aero/PLkZjai-2Jcxlg-Z1roB0pUwFU-P58tvOx

[@timothymbulambago]

Thank you Jeffrey. This has been so helpful. Thanks.

[@holyshit922]

I prefer firtsly reduce to triangular matrix to be able to see determinant and eventually stop calculations when it equals zero

[@primetrader5062]

This channel is greatly underrated! Probably the best videos about matrices on youtube!

[@goodwavedata]

These are definitely awesome. I'm self-learning all this material and one thing that's working well is some "all-source fusion." I've mixed these w/the 18.06 lectures, Khan, James Hamblin, and Math The Beautiful. Hearing it in different ways, from different instructors, helps to make it click for me. Sometimes I think 18.06 assumes too much from the beginning, but I'm planning to back to those after I've gotten through all these other series.

[@seth9301]

Too much man. The value here is enormous

[@noorelhoudaa28]

You're totally right

[@cricticalthinking4098]

I always look for one of these before tackling homework on a related topic. Gets me in the correct mindset.

[@flaguser4196]

yeah, absolutely. i got to invert a matrix with my own code for the first time! major life milestone. haha.

[@tharunnilanka840]

I was sleeping when this part going on my campus lectures. But no worries sir Jeffrey is here for me. love and gratitude from Sri Lanka.

[@thanglee2345]

how does this only has 4k views?? I'm so glad I stumbled upon this channel. I'll share to my classmate for sure ! greetings from belgium !

[@janeahdavis]

OMG... I am so glad I found your video. Thank you so much. This has been a struggle and you made it very easy for me to understand.

[@estherngeso4544]

Sir thanks for making me understand this...I've really been struggling 🙏🙏🙏

[@sermonseeker]

Thank you very much, i was having linear algebra exams and i watched this few hours before. And it has helped me

[@pini1946]

Neither Coursera, Khan Academy, Platzi nor the many websites I visited before could provide an explanation this clear. Thanks a lot.

[@TiktokBeats]

Thanks for this it's a big help for me for my linear algebra

[@nathanielnaidoo1811]

Thanks Prof! Love your style of teaching

[@chvilohith4133]

excellent video sir please upload videos like this

[@pietrarualfred9209]

life savior, thank you very much for this video

[@user-yx5wd5yy6h]

awesome tutorials! thank you.

[@rachidnajib1013]

Hello thank you for this video. Can we use the exchange of rows in this algorithm.

[@toodles8397]

My lecturer rushed through this part for us im so thankful your videos sir, otherwise there would be no hope for me

[@uddeepisiwara1358]

Clear Easy to Understand❤

[@muazzamali3659]

Respect, Thanks

[@habib97se]

Thanks Jeffrey

[@renaldferraj2658]

First divide the first row by -3 and you can start making the diagonal by. It's much easier and there is less confusion.

[@nargizpashayeva8549]

Thank u so much !!!

[@chandamandona1940]

Thankyou Sir

[@muheezolamilekan9818]

thanks alot

[@flaguser4196]

Thank you very much for your clear lessons! I was able to code my first matrix inversion from scratch, in less than 20 minutes. I coded in Octave (Matlab clone) and it is actually far simpler than what I used to imagine (reading through Numerical Recipes in the past made me think it wouldn't be simple...). It may be silly given Matlab already has it's own built-in "inv" function, but my goal is to eventually port my code to other languages while avoiding the unnecessary hassle of overkill linear algebra libraries. Octave is also convenient for checking that I got the algorithm right. After inverting several random matrices, I noticed that even if the pivot values are zero (where I just abort to avoid division by zero), Matlab's "inv" function can still compute an inverse. As far as I have searched, this is where row swapping or partial pivoting comes in. I wonder whether you have covered this somewhere. Thanks.

[@ProfJeffreyChasnov]

I cover partial pivoting in my Numerical Methods for Engineers course.

[@AJ-et3vf]

Awesome lecture sir! An alternative and probably more effective to do this sir would be to do an LU factorization since we are effectively solving 3 sets of 3x3 linear equations, i.e. we have the same A matrix thrice. LU factorization comes in handy for problems like this with different b vectors for the same A matrix. Otherwise, still very nice lectures sir!

[@ProfJeffreyChasnov]

Nice comment!

[@chuadaniel]

how do you solve it if the matrix is not a square matrix which i believe means 3x3 or 2x2 or 4x4 or 5x5 etc

[@ProfJeffreyChasnov]

Only square matrices have inverses.

[@prathamgupta4900]

method is nice but how do we mathematically proof the this method give inverse matrix everytime

[@footballistaedit25]

I also ask this to myself

[@oshadhaedirisinghe1455]

♥

[@zarbose5247]

How is he writing backwards?

[@DIOBRANDDDDOO]

Because he is kid the finger

[@mohammadlatif4924]

Sorry Sir, first make 1 to diagonal and use row operation and onward similarly will be easy.....

[@anushreegairola2291]

Sir why we are learning to find inverse .

[@ProfJeffreyChasnov]

Good question. Mainly for theoretical reasons.

[@Alex-bc3tt]

Plenty of reasons... such as solving for a system of linear equations by putting them in the form Ax=b and then let x = A^-1b

[@kushaljayaswal4255]

waltah