Product of elementary matrices

Writing a matrix as a product of elementary matrices, using row-reduction
Check out my Matrix Algebra playlist: • Matrix Algebra
Subscribe to my channel: / @drpeyam

[@adolfocarrillo248]

Dr. Peyam Thanks to your presentation I can derive the mechanics of the "Inverse of a product of two or more matrices". Take care dear Mathemagician!!!!!!!!!!

[@neilgerace355]

And also in matrix arithmetic you have to decide whether you want to put your left or right sock on first.

[@davidalexander4505]

I really enjoyed watching how elementary and irrefutable this method was. This result sheds an interesting light on how few linear transformations from R^2->R^2 there are. Indeed, it's clear that there are only as many matrices as |R^4|=|R| and hence only this many linear transformations. Awesome video!

[@aaronchao1972]

Yes, that's exactly what I am currently learning in my Linear Algebra class in my freshman college year 🙂 I still get a little confused so I have recently been doing more practice problems and seeking more professor and fellow-mate help.🙃

[@MrCoolerMan1]

I don’t know what’s funny, but it sounds like you’re having fun! XD Thanks for the explanation:)

[@qubix27]

Hello Dr. Peyam. I noticed, that you changed the name of your channel recently. Why? Is it not longer a show?

[@drpeyam]

Haha, I did! I think Dr. Peyam is shorter and slicker :) It’s still a show, no worries!

[@VechtMalthos]

@@drpeyam You just need a snappy intro. "You're watching.... THE DR. PEYAM SHOW!!!! ...Starring.... DR. PEYAM!!!" (queue catchy jingle) (cut to various sound bytes) "USE THE CHEN LU!!" (fade-out jingle) "Hello! Thanks for watchiiiiing! So, last time..."

[@NedStarkZA]

@@VechtMalthos I agree,,, kind of like Dr Sheldon Cooper presents Fun with Flags by Dr Sheldon Cooper

[@ManiFunctor]

Elementary matrices my Watson!

[@norman.20]

Greetings doctor Payam jan! Your method in algebra is really smooth and cool. keep it going. Surely many enjoy it.

[@mehdisi9194]

Thank you dr. Peyam. But is this decomposition namely LU decomposition unique for square matrices?

[@drpeyam]

No, since the row-echelon form of a matrix isn’t

[@TheGiladklos]

My linear algebra teacher uses the same example with the socks and shoes for the iverse product

[@sujaldhungana3216]

excellent video :) thank you.

[@ididagood4335]

Dr. Peyam! I have a question: I tried row reducing a matrix using 2 different sets of row-reducing steps, and when I multiplied the elementary matrices of the steps for each set together, I got the same matrix for both sets of row operations. Is this true for all matrices and all ways to row-reduce? Is there only 1 matrix that transforms a given matrix into its row-reduced counterpart? When I say I used 2 different sets of row-reducing steps, I mean that for one set, I mainly took multiples of the 1st and 2nd rows to row-reduce the whole 3x3 matrix and for the other set, I mainly took multiples of the 2nd and 3rd rows to row-reduce the 3x3 matrix.

[@anjanasagar2123]

Yeah it will be true for all the different set of elementary matrices. Because row reduced echelon form of any matrix is unique, no matter how you arrive at the row reduced form.

[@vijayank1170]

Dr peyam, you seem to concentrate more on leniar algebra. Can you please give a lecture course on differential equations, including lots of practice problems.

[@drpeyam]

There’s a playlist for that

[@vijayank1170]

@@drpeyam thanks Dr peyam, I didn't see that. Let me check that Playlist.. Also can you suggest any book selections for studying differential equations.. It would be really helpful.

[@drpeyam]

I love the book by Hirsch Smale Devaney

[@ethancheung1676]

What does elementary matrix means? Simply the matrix form of a row reduction step?

[@sugarfrosted2005]

Yup, row or column operation. They can also be scaling a row or column by zero iirc.