Inverting matrices (part 2)

[djp117]

WRONG TERMINOLOGY! The adjoint or adjugate is the complex conjugate of each element then transpose!!!!

[CWCWwang]

@ 11:54 bottom left corner, the 2 should be positive because of the chart plus and minus chart he wrote on the top right hand corner!

[nikmuic]

well I hope this can prevent my brain from degrading too

[WormySauce]

WHAT VILE SORCERY IS THIS?

[jonescomplete]

@WormySauce THIS IS SPARTA!!!

wait no thats not right at all...

[pjgmorgan]

who discovered that this worked!? mental

[boxerek123]

after this video i can see the matix!

[dqds]

What is this sorcery?! Feels horrible to follow formulas without knowing why.

[kv310]

@dqds Then go and seek the proof so you feel better, you can find it in any linear algebra book.

[JaLalalover]

Uhm, how do you use this  in real life? -_- I so don't want to learn this but oh well! Dear school, I love u!!!

[89lovely89]

@JaLalalover I'm in 3rd year at uni. This is suppose to be knowledge when dealing with certain types of encryptions and decryption in network security (Information and Technology degree). This is only one example and i'm sure there are many others.

[Fukkensaved]

@JaLalalover

It has hundreds of applications through Linear Algebra. Matrices are almost limitless in usefulness from engineering and computer science to economics and physics.

[mrseddy14]

If you have a graphing claculator there is a really easy way to do this........ Skip all steps...... Put your matrix in as a 3x3 and fill the number in. Then get this on your calculator screan [A] and use the x^1 button on the left of the calculator so it says................. [A]^-1.............. push enter. Answer... Easy as pie :)

[jameswell92]

We need lecturers like you !

[likson2003]

Thank you Khan. I am from Hong Kong

[TheXatheron]

It works =D

[nitro1821]

i love you man!!

[MarcoOrBust]

whats wrong with hairy?

[biruktayit]

Its easy because he always chooses easy numbers. Its easy to solve inverse matrix with 0 and 1.

[jaimix697]

There's an easier way 

[jassbansal]

@jaimix697 watch part 3, i believe thats the easiest way

[mo3ius1]

keep pressing 9:15

[danielzhang0]

@mo3ius1 i dont geddit

[mo3ius1]

@danielzhang0 you can DO IT

[TheLoveformankind]

watching

[emirguy]

9:15 for words of wisdom!

[bluestarr78]

My professor is doing all theory and I haven't even heard of a "determinant" or a "coefficient matrix" to solve this problem - very useful!

[bluestarr78]

@MakingCables - DITTO! This really isn't anywhere near as difficult as I was making it. I am going to watch all of his videos. I just hope he covers most of my linear algebra book lol!

@drkmashcore - yes, only square matrices can be inverted

[greeneyedutchman]

I love my numbers non-hairy

[MakingCables]

55-minute lecture, and I leave the room scratching my head.

17-minute khanacademy video, full understanding.

Thank you.

[drkmashcore]

just a question, can you only get the inverse of a matrix if it's a square matrix? or can you do it with any matrix with any number of columns and rows?

[iKennayyy]

One of these took me around 30 minutes to do.....

[tedoymisojos]

Thank you so much! I have such a hard time studying

[TheProoMas]

I'm amazed you didn't make a mistake =D. Got the identity matrix when multiplied those two together ^^

[osx101]

so good I have learnt sth from ur vids

[mimmoon16]

dam this is good

[123alankar]

at around 12:51 i wonder what falls in the background..... :-p

[fourhire]

haha only took 17 minutes...

[DotAis4Noobs]

I love you

[HawkBladex]

you are my GOD

[LeBadman]

I can't believe they teach this stuff in highschool. Uni math is more like.. graph theory, base 5 numbers.. etc.

[LeBadman]

oneoenoeneonEONEONEOENOENEONEO­NE

[LeBadman]

Why do you use a mouse and a computer instead of plain simple paper and a pen?..

[iM0NzT3R]

you saved my life but when i solved at the end it did not work -_- it was like:

1 0 1

0 0 1

0 0 1

[moomoos99]

I eat inverted matrices for breakfast u dumb mother fuckers.

[gdogfolife]

wow thanks alot, this is way easier than having to do row operation with the 1 0 0 in the first row and so on.

[iampoy]

wouldn't pass my exams without your help! THANK YOU!

[tiffhyw]

Thanks you saved my life

[StaticShock1100]

Math test tomorrow, Khan is like a life jacket, its the only thing keeping me afloat. Now, to cram and crunch info for the next hour and a half. *CRAM CRAM CRAM CRAM CRAM*

[lovexoxomiley]

thanks for ur very helpful videos mr.....(dono)

[pjtechy]

we have Matrices for another two years in CS .. U saved my ass in the exam .. love ur videos.. .

[CharlieTan84]

Hello Mr Khan

Thank you very much for this awesome lecture.

[colverjustin]

"non-hairy" - well played Sal

[RippzZ]

Why don't you use the gaussian elimination method with a second matrice on the right. Diagonally 1 1 1 and the other values zero?

[angelwings2323]

You have no idea of how much of a lifesaver you are!

For the past 3 weeks I've just been going "WTF is this?!" in my math class... This is much simpler then the way my teacher taught me, her way is so confusing, It hurts my brain to try and remember!

Thank you!!

[aeonthailand]

I love you ..Thank thank!!!

[DesuChanXD]

How is it possible to dislike this video?

[scottdylan20]

no wonder why computers where invented

[OMFGCMON]

@blueeyesofgrey I believe you get the same answers. This method is just the method used before they realized row reduction works to get the Inverse Matrix. Well at least that is from my still learning Linear Algebra understanding lol

[ria75002]

hhahaa wtf? 65,179 views on math?! kay Im out(;

[gabe562]

So much better than the stupid row operations.

[L0gic3rror]

Your videos really help me, and i am sure not only me, I thank you so much, you really teach very well.Thank you again!!!

[LAnonHubbard]

Really good explanation.

[scruff76]

YOU ARE AWESOME!!!!!!!!!

[AdThaDon2k8]

this kind of math grows an appreciation on me to folks that do computer science and technology that requires these algebratic applications :]

[inuyome1008]

This is DEFINITELY better than how my COLLEGE TA tells us to do it... Thank you SO much.

[Diastro3D]

Thx, clear & simple!

[robertfox1975]

Fantastic sal...

[fluffywhee]

Have you a method which uses Elementary row operation? thanks!!

[stothek2]

bro WAY TO SMALL

[coppernicuss]

thank you

[lordswit6666]

this is what my Engineer tutor told me... unlike my teacher in ateneo.. she does the row x bla bla bla which is so confusing.. thanks anyway

[bbhardoin]

if i fucking hate matrices, but found this helpful, should i like or dislike this video?

[fizaanTech]

@bbhardoin like, and please don't use bad language. kids watch these videos.

[stothek2]

@fizaanTech if anyone is watching vids on linear algebra they're old enough to know how swear you fuckin dirty cow

[fizaanTech]

@stothek2 Swearing is for uneducated people with no other choice of words because their vocabulary is so small. If you're watching these videos, you're educating yourself. I can swear if I want to, I just choose not to, especially in this kind of setting.

[RandomPerson150]

Oh... my... GOSH!!! I UNDERSTAND MATH!!!

[SwitchingDisguises]

What happens when you multiply the top part of A with the matrix of cofactors and it equals 0? Does that mean there is no inverse of matrix A?

[hedonism13]

Thou hath conquered the mighty 3x3 matrix inversion. Huzzah!

[bla7091]

My professor told me to do this by row operations to turn the original matrix into an Identity Matrix, repeating the same steps in an equally large Identity Matrix that would then turn into the inverse matrix.

Way way harder than using determinants

[ABCba5tard]

ur the saint in math!!!!!!!!!!!!!!!

[simplyalif]

Ouch my head hurts

[BattenburgBoy]

you are a true hero!

[frother]

How do you get 4 degrees from MIT and not understand Undo?

[tttooommmyyyy]

your videos save my ass every single time! it's amazing. i don't even bother showing up in class anymore. i just learn from your videos. moreover, my classes are in spanish and i still feel more comfortable watching these in english.

thanks!

[Keablerthegreat]

Dude....Props...

[skyfaze]

hey that step is simliar to the cros product

[madscirat]

If geeks could have saints, Sal Khan would be one of them.

[pure5abi]

@madscirat u mean if Geeks could have Gods!

[CaptainFluffy6644]

"if i keep doing this my whole life it'll stop my brain from degrading"

one of the many salman khan win moments

[MrJavaHelp]

Sal, I checked the inverse matrix you made by multiplying with the other one. (A * A^-1) and I got the Identity matrix, I. So you didnt make any silly mistakes! yay!

[nivvig]

quick question... why did you calculate the matrix of minors?

why didnt you straight away calculate the det|A| and then the adj

[UndeadTheta]

@nivvig the adjugate is the transpose of the matrix of cofactors, which comes from the matrix of minors.

[WindyCityOfSails]

I'm back in school as an adult. B.S. Physics. You have given all of us an additional supplement with which to augment our learning resources, and for that I thank you. A suggestion from a patron of your videos: Lecture series on Vector Calculus? Thanks again for sharing your knowledge.

[ActiveCamouflage]

What he said, a series on vector calculus would be very much appreciated.

[Ykoahi]

mother of god.

i'm so happy the other way of doing this exists.Cause that is a hot mess.

[MiniGeek31337]

I got it!

Thanks a lot!

5* again

[ibanez1andrew]

Thanks.  you made it a lot clearer then teacher!

5*

[pinaygirl23]

OMG dude, THANK YOU!!! you just saved me

[ndog33]

Why is the adjoint the same as the matrix of cofactors? does that mean that i dont have to "transpose" or my better guess, is that this is a special case?

[amjPeace]

The matrix of cofactors just so happened to be symmetrical around the diagonal, but that won't always be the case.

Happy New Year, ndog33!

[theonlyrealshark]

its a special case cause the matrix is symmetric he explains that in the video.

[hulio1987]

very good explanation!ty

[cndiixx]

this really helped!!!!!!!

[will3330]

There is a different way of doing it by using Gaussian Elimination with the nxn matrix and the identity matrix and trying to manipulate it so that it ends up the identity matrix and then the (nxn)^-1 matrix

[onmyblindside]

I used this video to answer a quiz question and I arrived at the correct answer! thank you for posting this informative video.

[quantomic1106]

I hate matrices.. its easy as you make careless mistakes.

[NeoXC]

Great!  I've been trying to figure a way to do inverses in a systematic way, without doing all of that multiplying, substituting, changing rows and columns gobblygook. My pre-calc teacher is threatening to put a 4x4 or 5x5 matrix on my next test and this would save me a bunch of time. ... : S

[Soulj4h4Christ]

3x3 Matrices are a mess. WOW!!

[david0aloha]

I didn't do any matrices in high school (though I did my gr. 11 and gr. 12 pure math classes in the same year while they were changing the curriculum around) and you're saying that they do this in many curriculae in the US? I'm doing this now in university, and I'm able to wrap my around it fairly well, but man is it tedious (and I'd imagine hard to understand if you didn't see the purpose or are unable to visualize what it represents).

[lorifix]

I can actually understand these lessons. These are going to save me on my exam. Thanks.

[jeestudent007]

I am a retard. But I understood this. Thanks

[TajikThunderstorm]

this video is fanatastic, but its very confusing to digest , though with practise it should be easier.

[tweakedmofo]

So very helpful

[andreiduffy]

i have another method of calculating det (A) where you don't need the corresponding co-factor.. but i guess it's easier the way you did it...

[teespoon1234]

good video

[lyaskoff]

Hey Sal, thanks for the great video! :) But how do you apply this for a 4 by 4 or n by n matrix?

[shoyb]

sal do you have a fish tank?

[smokethatbong]

Ok I have tried this method with 2 different matrices now and it has worked for neither. It only seems to work for yours because you are using such a simple staarting matrix. I like your videos but the examples you use are far too simple. The same with the gausian method, it is much much harder with a larger numbered matrix.

Please show me how this method works for the following matrix.

2 1 -1

5 -2 1

-1 -4 3

[Rejpi]

smokethebong: Try one more time using exactly the same method, I have done your example using khan's presented method and the result is all good. (I have checked it using calculator). You had to made some errors while computing negative numbers. There are some fractions if that cheers you up :)

[dohpaz42]

I don't know why, but this method seems to be easier than the Gauss-Jordan method for me. Thank you for this video!

[59011]

Matrices trigger protests in my brain.

[dre893]

Thanks, explained it very well.

[TIABTS]

Why dont you use the rules of Sarrus???

[8dimensions]

"It will prevent my brain from degrating" That was funny :D Thanks again for your hard work, you're the modern kind of a superhero.

[qbanguy7]

thanks a lot for this technique. I think this is less confusing than the elementary row operation.

[cianestro]

Agreed. Inverting an nxn matrix utilizing determinants is child's play compared to elementary row operation tomfoolery on this scale.

[PeinItachi]

@qbanguy7 explain elementary row operation to me in the comment box... lol jk

[CoauthoredStaircase]

Question: shouldn't the adjugate matrix have a 1 at row 2 column 3, instead of a -1?

[Zephyruu]

MATRICES ARE A WAR OF ATTRITION!

[shrey321]

thanks..that helped

[toapeth]

I multiplied them and it came out correct, Nice Work Sal!

[zkuzio]

thanks man....ur a legend.....trying to figure this out for a long time.

[zkuzio]

ur a fucking legend......i spent a whole yr trying 2 figure this out....got my exam in 2 days n u finally helped me.....cheers mate.

[vermichou]

Really great, well explained, simple !!

I've never learnt that before and following the steps with you gets my head around matrices !!!

Cheers!

[rb44]

haha man thx i just needed a refresher for my exam...lol when u made the first matrix i was like...thats symmetric ...ur gonna get a symmetric transpose and i was thinkingg that if u had to show how to do a transpose it was gonna suck for ppl haha but nonetheless GJ

[DeViLiN888]

"It will prevent my brain from degrating" :D Yes, matrices are consuming my brain :)

[ddeny22]

so tedious, i hate IB for expecting us to remember all of these steps. thanks!

[liyasec1]

I <3 your voice

[Winsunn307]

Great work, Sal.

[the988]

Good job ! U got it right of course, I multyplied it out and as expected it gives me the Identity matrix .nOW i UNDERSTAND WHY U DISLIKE THEM..I JUST HOPE ITS NOT GOING TO BE ON MY MIDTERM !THANX A LOT, UR GREAT !

[3807312]

thanx ALOT :D

[riccocz]

very nice, thx

[51andCounting]

I love you man! That was so helpful! You just hopefully got me 6 more marks for my exam :)

[jellyjam10534]

at least i know it isn't me who only thinks this stuff is hard lol

[killersdeat0]

Thanks so much... (my brain hurts now) but at least i understand it now..

[dejawolf]

thats sorta like playing sudoku.

[Toharvard]

coo

[XanxenigmaX]

THAT IS EXTREMELY HELPFUL! thanks! XD

[chopperhead2011]

Only 17 minutes!!!

[darkwspyder]

Thanks! lol I recently learned matrices in pre cal in high school!