Linear Algebra - Lecture 24 - Elementary Matrices and Inverses

In this video, we will discuss elementary matrices and their relationship to invertible matrices. We will prove a theorem that explains how to tell when a matrix is invertible, and how to find the inverse of an invertible matrix.

[@Brahma2012]

It is a elegant explanation of elementary matrices. Thank you James

[@VersatileAnthem]

sir ,you are just awesome .the most clear explanation i got....thank you so much.may Allah give you blessings

[@ahmetkarakartal9563]

türk müsün

[@steveying1305]

This is the best explanation for the means of deriving the inverse matrix, thanks so much James!

[@kerduslegend2644]

My guy!! You explain it better than my college professor.. All my profesor did was "here's your equation, don't ask how you get it, just use it" Like... Bruh💀

[@cgmakesbeats]

So much better than my professor!

[@SaiyanBranch]

In the beginning I think you meant adding -4 R1 to R3

[@lattice737]

4R1 + R3 leaves one value, 1, for the first pivot column. -4R1 + R3 would leave -8 and 1 in that pivot column

[@baguettebaguetteneverforge1758]

@@lattice737 Can you explain how It would leave -8 in R3's first column?

[@lattice737]

@@baguettebaguetteneverforge1758
Just to be clear, I was saying this is the wrong answer:
-4R1 + R3 =
-4 [ 1 0 0 ] + [ -4 0 1 ] =
[ -4 0 0 ] + [ -4 0 1 ] =
[ -8 0 1 ]
The correct answer is:
4R1 + R3 =
4 [ 1 0 0 ] + [ -4 0 1 ] =
[ 4 0 0 ] + [ -4 0 1 ] =
[ 0 0 1 ]

[@mariusmusicandscience]

@@lattice737 You're totally wrong, stop spreading false information. The video itself confirms he made a mistake at 2:55. There is a scaling of -4, not 4 as you mention. I hope it is clear now for anyone reading this that was confused.

[@lattice737]

Marius van Gent I see what you mean at the time stamp. I’m obviously not intending to spread misinformation if I’m taking the time to show my work, jackass

[@crazyguy7665]

best explaination ever on elemnatary matrices.....

[@kabirbaghel8835]

are u crazy

[@7906jun]

13:35 I wish you showed all the steps instead of talking over and only writing the final answers.
Otherwise, very helpful video thank you for your time .

[@piyush501]

What a quincidence I m watching this video on 7 June 2020 ... Exact 2 years after this vdeo uploaded 🤣🤣😎🙂🙂

[@dhanamillionaire8936]

Thank u for explanation...this really helped me to understand ♥️👍

[@Rand3mAnclrew]

Thank you for making these videos

[@adinandyala]

Hey! I didn't understand the last part (15:00). Can anyone please break it down for me in simpler terms...

[@GenuinePeacefulTimes]

Great explanation. Thank You.

[@childrenfunfriend6101]

Thank you sir for ur video

[@samuelromero1763]

Thank you my teacher did not explain this at all.

[@wmd5645]

Thank you, considering an arbitrary matrix is the best way to describe elementary matrices! Wish I found this months ago.

[@HAHA-rf4dc]

Thanks!!!!! its helps a lot!

[@aliosmanmusuloglu7382]

Thank you so much, James :) It is the best explanation i've ever seen.

[@ryanjackson0x]

Is there a quick way of finding A=EU by hand?

[@hannatr3135]

Thanks...... So helpfut

[@MrPowderhound9]

Is it possible to find the inverse of an mxn matrix or do inverse matrices only exist on square matrices?

[@HamblinMath]

Only square matrices can have inverses.

[@ghsjgsjg53chjdkhjydhdkhfmh74]

@@HamblinMath thank you!

[@ryanjackson0x]

It is possible to have a right inverse for an mxn matrix. (AB=I, where A is mxn and m

[@kellypeng6371]

Thank you so much 🙂🙂🙂

[@GeorgeFloyd2]

THANK YOU!

[@michalhellman7214]

Incredibly appreciated. Very well done video.

[@harry-fl6tf]

you saved my ass Thanks!

[@muhtasimrabib9795]

Don't you mean adding -4 . row 1 to row 2

[@HamblinMath]

Can you give a timestamp to where you think you found an error?

[@HamblinMath]

@@frettenbrot Ah you're right, that should be adding -4 times R1 to R2

[@haniamahmood-e8r]

4:14

[@ibile2922]

Why do I still pay in expensive university???