How to find the inverse of a 3 by 3 matrix (3 methods you need to know)

[@aleksgornik]

Gaussian elimination sucks, it’s a bit trial and error and if you take the wrong route you go into a black whole and can’t go out of it

[@ProfOmarMath]

It's fun that you're embracing linear algebra

[@blackpenredpen]

I am trying! It's been over 14 years that I haven't done any of it, lol. So I am only starting with the computational part first and then I will get into the more conceptual part.

[@ranjitsarkar3126]

@Leonhard Euler I am a real big fan of you Mr. Euler. But I cannot subscribe your channel. Because you are faking

[@aashsyed1277]

@@ranjitsarkar3126 who?

[@talentedtobi]

The last method is Gold. Thanks so much.

[@parasgovind6271]

You have the best timing!!! I literally learned this topic a few days back and always complained about how long it takes! Your third method is awesome! Thank you!

[@youkaihenge5892]

When you drew that big matrix for C that face you made was hilarious knowing we all are suffering from the inverse hahaha

[@blackpenredpen]

lol, imagine if it was a 4x4 matrix

[@puneetmishra4726]

@@blackpenredpen The third way could work for 4x4 matrix as well?

[@virajagr]

@@puneetmishra4726 I guess it will work when n is odd. When n is even, the plus minus sign would mess up.

[@MA-bm9jz]

Another method would be from the characteristic polynomial,by writting A^(-1) as a linear combination of A and A^2

[@wduandy]

How?

[@MA-bm9jz]

@@wduandy so a 3×3 matrix has a characteristic polynomial like this A^3+a_1*A^2+a_2*A+a_3*i=0 ,multiply by A^(-1) and we get A^2+a_1*A+a_2*i+a_3*A^(-1)=0 and from there you get A^(-1)

[@SimonClarkstone]

@@MA-bm9jz How do you find a_1, a_2, a_3?

[@MA-bm9jz]

@@SimonClarkstone you compute the characteristic polynomial,det(A-x*i),but since A is a 3×3 -a1 is the trace(since the sum of the eigenvalues is the trace),-a3 is the determinant(product of eigenvalues),all those observations come from vieta's formula,a2 is a bit more tricky,is the sum of all 2nd degree diagonal minors,or just compute det(A-x*i) and those a_i will come naturaly

[@SimonClarkstone]

@@MA-bm9jz I don't know enough linear algebra to understand that unfortunately.

[@jordimayorgisbert6490]

I have no idea about the pretty 3rd method !!! Thank you 🙏!! I’ll give it to my students next monday !! Very nice !! (Like the D.I. Integrate method 😉)

[@blackpenredpen]

Thanks for liking! Cheers!

[@SahilSharma-nh8tr]

My teacher already taught me these methods 😎😎😎😎

[@megauser8512]

I like the 3rd method the most too!

[@geosalatast5715]

There's a guy with a goat beard who holds a pokeball, has the Picasso painting The Scream and is talking about matrices... Pure Excellence! Greets from Greece!

[@ytsimontng]

And runs Marathons 🇬🇷

[@DarthJeremy364]

please note i do not think the last method applies to matrices greater than 3 x 3

[@jeffayako]

i love the last one u make it look really easy i will try writting a CPP code to compute the inverse using that algorithm

[@tomatrix7525]

Peyam - Funniest math teacher. Bprp - Coolest math teacher.

[@egillandersson1780]

The first way is the more "theorically understandable", but the third way is the coolest to perform. Once you have computed the adjugate, you can also ignore the last raw and column and use the centre to compute de determinant (if not previously done). So, an "all in one" method !

[@iRam8UnderScore]

Sorry do you mean removing the first column and last row? Because that works out, whereas what you mentioned doesn't work. ??

[@farkasmaganyos]

I really appreciated the 3rd version! Many thanks for that!

[@MrKA1961]

Szerintem is ez a nyerő.

[@21croz]

I have an Algebra exam next week, really appreciate these videos you are uploading. Greetings from Chile!

[@dookey6099]

I just finished this topic in school , finding the inverse of 3x3 is such a pain for me because I always make stupid arithmetic blunders. Just got to be careful

[@GreAse0MonKey27]

the last method is the life saver!!! :))

[@AlfredPros]

That last trick is so cool! I wish my lecturer taught me about it!

[@TobyBW]

Watching this while doing my linear algebra homework on inverse matrices

[@tomatrix7525]

Ditto

[@SwordQuake2]

The second method is best. You won't need to calculate the determinant separately if you don't have it.

[@XgamersXdimensions]

I took Linear Algebra over the summer (and passed!) but I’ve never seen the 3rd way! Very useful and would have saved me a lot of time

[@KN-tt7xu]

That 3rd method is actually very useful, thank you for showing that

[@francine8563]

thank you so much sir, you made it look easier! I just want to ask a question, regarding the 3rd way 24:30, can I use it still when solving for determinants with 4 x4 or more matrix?

[@wanlitan7406]

24:25: "It's not a new way" Title: "Inverse of a 3 by 3 matrix (3 ways)"

[@nationalstudyacademykim5030]

As a HS math tutor, you are very entertaining!

[@SHASHANKRUSTAGII]

Unfortunately, I knew this before u could upload this, but it is always love to see you. PS: You and Quang Tran look alike And I love you both. One for Maths One for Mukbangs

[@mmh2695]

This video is so good, now I'm ready for tomorrow's exam, thx a lot

[@dr.rahulgupta7573]

Sir I found 3'rd method the best .Congratulations for it .DrRahul Rohtak Haryana India

[@pedrokalume2473]

One more reason to start watching bprp is that he is now making Linear Algebra videos

[@trueriver1950]

This technique applies to any sized matrix with an inverse. It is the matrix algebra equivalent of doing simultaneous equations as usually taught to students before they meet matrices.

[@TechnoCoderz369]

Thank you Very much!

[@BCS-IshtiyakAhmadKhan]

The method used in the thumbnail was already taught by my teacher last year

[@aravinds3846]

Another way to find inverse is by using Cayley-Hamilton Theorem, which gives |A -λ I | = 0 , where I is a unit matrix. When we evaluate this determinant we get an equation of degree n , where n is the order of A. The equation is in terms of λ, so replace it with A. Voila! we get an equation with variables being the matrix and constant is the unit matrix. Multiply by A inverse and get simplify the rest o the terms to evaluate A inverse

[@chunfaimok767]

I am actually looping 9:40,13:42,15:40 those charming laughter

[@ItsMeTheUser]

3nd way is very clever, thanks Steve!

[@drpeyam]

Woohoo, I’m inverse ready 😇

[@vishwanraja666]

do you play the sims ?

[@trueriver1950]

Fourth way: apply the BPRB technique but the second matrix is not the unit matrix but this: Det 0 0 0 Det 0 0 0 Det This gives you the transpose matrix in the second example. Remember to divide the integer matrix you get by the determinant of the original. You can either divide each element, or just write a scalar multiple of (1/Det A) in front, depending what you are about to use the matrix for. This offers an insight about why there is no inverse when Det = 0 because you'd be dividing by zero... I prefer this fourth way

[@6754bettkitty]

You should cover pseudo-inverses!

[@angelxd7019]

Gracias por compartir sus conocimientos maestro redpen 💪🙌

[@AttilioPitt]

This is AMUUUSING! thank you! i love this trick

[@chawkichalladia1812]

i remember being good at matrix in college. i remember doing that second method. this was more than 5 years ago. the only chapter that gave me hope of being good at math xD

[@rezamiau]

Great! but in the second method, you could use Cofactor Matrix to evaluate Determinant easily! so I think the second method is much more faster than the first one.

[@archerdev]

matrices bless you man, thanks for this dead cool video. Much appreciated

[@tayserbinjafor7697]

It's not adjugate, it's just adjoint.

[@saurabhin]

I know all of the method. But, i like your way of teaching ♥️

[@sugarfrosted2005]

The adjugate is good for rings without inverses because it always works. Though it might not be a real inverse, but good enough in a lot of places.

[@lesnyk255]

I think I like method #3 the best for manual longhand calculation, but #2 as the easiest to program..

[@coleabrahams9331]

I always used to use the second matrix. Thx for this

[@yuliiavideo]

The third way is excellent. May I teach my students this method?

[@arnaldosantoro6812]

11:00 "either you like it or you hate it" Clearly hates it

[@ose31]

Very good...👏👏👏👏👏👏from Brazil...

[@DilipWoad]

All the method i was knowing 😅 but i love...i taught u might have other shortcut .....the 3rd is my favourite i use it every time its easy

[@daphenomenalz5784]

Great video...actually Today i was trying to find some more ways to calculate the inverse of a matrix and you helped me a lot. thank you...but now I'm wondering how to compute inverse of a (n by n) matrix where, n is any unknown positive integer Please share how to do this

[@blackpenredpen]

Thank you for you comment. I think, unfortunately, once we get a bigger matrix, we have to use either method 1 or method 2..

[@rocksbit]

Superb video brother

[@shunmugasathishk9365]

The 1st method that you've done is Gauss-Jordan method

[@Olavotemrazaodenovo]

Congratulations from Brazil.

[@pauljackson3491]

For the 3rd method, the crossed out -4 is only used for the det. now? And can you actually start anywhere but 1,1 (where the -4 is) is easiest?

[@virajagr]

Can you do proof for second method? Thank you

[@holyshit922]

a_{n}=1 a_{m}=-1/(n-m)(sum(a[j+m]tr(A^{j}),j=1..n-m)) This will give you characteristic polynomial and from Cayley Hamilton we will get the inverse This is not as fast as elimination but faster than cofactor method

[@nex]

Here's the ‘how to determinant‘ video: kzbin.info/www/bejne/ipyxlneupLecobs (Maybe put that link in the description, 曹?)

[@jordimayorgisbert6490]

I’ve a little "improve", making the T operation over the A matrix at the first, and then work with it. You'll avoid the final arrangement for making the T. I'm based on the property Adj(A^T) = (Adj(A))^T. That's only a suggest !! ;-)

[@atharvasharma3492]

Love your videos man❤️

[@abhisheksharmavats8326]

3rd is nice

[@bbbeware]

just happen to be taking linear right now so thanks for uploading! w00t w00t

[@virajagr]

Can the 3rd method be extended for higher order matrices as well? That is, copy first 3 columns and rows for 4×4 instead of 2 which is for 3×3. And then take determinant for each 3×3 matrices formed inside

[@ShinichiKudou2008]

I think that will work for sizes of an odd number (but not even number) because when a column in a square matrix of size of an odd number is shifted to the opposite end the determinant doesn't change sign.

[@virajagr]

@@ShinichiKudou2008 ah that makes sense, thanks

[@debilista]

21:00 MAH PROFESSOR IS GONNA MELT LOL

[@therealgoat3367]

"6 - 2 is... Why is that so hard?"...FELT!!!!

[@nickk4125]

The last one really made me happy

[@AttilioPitt]

The last method is very beautiful for optimazing the inverse. I really want to use it in an exam, but i think that i need to demostrate it. Could you please help me, please? Thx

[@DarthJeremy364]

What if you have a 4 x 4 or 5 x 5 or anything like and n x n where n is greater than 3. Do we still add the two columns and rows to expand the matrix for the shortcut method ?

[@higgs_boson2231]

You should do topology or abstract algebra!

[@sabriath]

I feel like a form of cryptographic key could be constructed with matrixes somehow.....maybe this will inspire me for the next week.

[@TranquilSeaOfMath]

Good presentation !

[@mathieus-c6761]

"dididididida" (delete this, delete that) Love ur vids, keep going on !!

[@redstoneplayz09]

I don't even know linear algebra but I am watching this because it seems smart.

[@Sergeak21]

WHATTT the third way is actually witchcraft. I have been wasting my time doing the second-way smh.

[@tamarpeer261]

It's the same matrix as the o e for the determinant trick. Is it special?

[@sambhav2727]

I have a doubt on characteristic equation of a matrix..For a 3x3 matrix A , we know that sum of eigenvalues = trace of A(sum of diagonal elements of A), and product of eigenvalues= determinant of A..For a 3x3 matrix,is there any significance of sum of product of eigenvalues taken 2 at a time? (i.e. (coeff of A) )

[@jackkalver4644]

Fun fact: Inverses can be found vertically using column operations.

[@francine8563]

i like the 3rd way the most

[@muskyoxes]

Is it a coincidence that one of the rows of the inverse don't have the nasty 13 denominator, or is something deeper going on? It's suspicious to me that, in the cofactor matrix, the multiples of 13 happen to line up.

[@laurensiusfabianussteven6518]

The sad part is i see this when i already completed my linear algebra course :'

[@l3igl2eaper]

I've always loved method two.

[@alexnoussi]

The 2nd way is familiar, and the third one is rather peculiarly interesting.

[@bsb0]

I wish I watched this video yesterday. before my linear algebra final😂

[@legendarytaj2054]

Way 3 is better if you have the determinant if not then gotta go with way 1.

[@lolegarcesfuster9090]

can somebody clarify the rigorous name of the 3rd method in order to pre-quote the method before solving the exercise.

[@hareecionelson5875]

thanks to this video I have coded an nxn inverse calculator in python. The determinant function was the trickiest, since it's recursive.

[@michaelempeigne3519]

Does this work for all matrices for n x n matrices with n > 3 ?

[@victorrodriguez866]

does the third method work for matrices with range > 3?

[@k_silentstorm9611]

dude thanks so much perfect timing

[@vinayaktyagi1001]

He : inverse of a matri- Me : *adj(A) / |A|* Adjugate ? I learned it as adjoint . Well both are same anyways so doesn't really matter

[@JRO512]

PLEASE DO LINEAR ALGEBRA PROOFS! I need some enlightening or else I’ll fail my class

[@drpeyam]

I have lots of playlists of linear algebra proofs in case you’re interested

[@KAMRANKHAN-xf7iq]

The Ist and 2nd methods are too hard! The 3rd one is easy and super tricky! Where the hell you learnt the 3rd method???

[@otheraccount5252]

Now that you have used a blue pen, are you going to rename your channel to blackpenredpenbluepen?

[@debunkosaurus8228]

Question: Do all of these methods work for matrices that are larger than 3x3?

[@smrtfasizmu6161]

The first method has to work for square matrices of any size (as long as their determinant is not zero of course)

[@mduya6239]

很久沒看你影片了，怎麼突然留鬍子了XD

[@smrtfasizmu6161]

3rd method is great. To me, second method is way worse then the first one because it is a lot harder to compute and it is harder to understand why it gives you the correct result in the first place

[@alihamad5246]

Cayley-Hamilton Theorem go brrrrr!

[@Mr_flewis]

Plz answer this question Q- integral of 2x^2.dx divided by (x-1) (x-2) (x-3)

[@davidgendron6955]

Try partial fractions.

[@Mr_flewis]

@@davidgendron6955 yes I applied that formula but

[@Mr_flewis]

Here 3 algebraic functions are present how can i solve?

[@BaiLanRenSheng]

What is the name of 3rd method?