Computing inverse matrices using Gaussian elimination | Lecture 12 | Matrix Algebra for Engineers
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- Опубликовано: 13 окт 2024
- How to compute the inverse of a matrix by computing the reduced row echelon form of the matrix.
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Thank you Jeffrey.
This has been so helpful. Thanks.
I prefer firtsly reduce to triangular matrix to be able to see determinant and eventually stop calculations when it equals zero
This channel is greatly underrated! Probably the best videos about matrices on youtube!
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.
Too much man. The value here is enormous
You're totally right
I always look for one of these before tackling homework on a related topic. Gets me in the correct mindset.
yeah, absolutely. i got to invert a matrix with my own code for the first time! major life milestone. haha.
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 !
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.
bro i slept when sir jeffrey was teaching, he is the slowest maths teacher i've ever met🤣
Sir thanks for making me understand this...I've really been struggling 🙏🙏🙏
Neither Coursera, Khan Academy, Platzi nor the many websites I visited before could provide an explanation this clear. Thanks a lot.
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.
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.
I cover partial pivoting in my Numerical Methods for Engineers course.
Thank you very much, i was having linear algebra exams and i watched this few hours before. And it has helped me
Hello thank you for this video. Can we use the exchange of rows in this algorithm.
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
Only square matrices have inverses.
My lecturer rushed through this part for us im so thankful your videos sir, otherwise there would be no hope for me
First divide the first row by -3 and you can start making the diagonal by. It's much easier and there is less confusion.
awesome tutorials! thank you.
Clear Easy to Understand❤
life savior, thank you very much for this video
Thanks for this it's a big help for me for my linear algebra
Thanks Prof! Love your style of teaching
Thanks Jeffrey
excellent video sir please upload videos like this
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!
Nice comment!
Thank u so much !!!
Respect, Thanks
chasnov!!
Thankyou Sir
thanks alot
method is nice but how do we mathematically proof the this method give inverse matrix everytime
I also ask this to myself
♥
How is he writing backwards?
Because he is kid the finger
Sir why we are learning to find inverse .
Good question. Mainly for theoretical reasons.
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
Sorry Sir, first make 1 to diagonal and use row operation and onward similarly will be easy.....
waltah