Solving Matrix Equations

This precalculus video tutorial provides a basic introduction into solving matrix equations. It contains plenty of examples and practice problems on solving equations with matrices.
Introduction to Matrices: • Intro to Matrices
Adding and Subtracting Matrices:
• Adding and Subtracting...
Scalar Multiplication of Matrices:
• Scalar Multiplication ...
Solving Matrix Equations:
• Solving Matrix Equations
Multiplying Matrices:
• Multiplying Matrices
__________________________________
Gaussian Elimination & Row Echelon Form:
• Gaussian Elimination &...
Gauss Jordan Elimination:
• Gauss Jordan Eliminati...
Gaussian Elimination With 4 Variables:
• Gaussian Elimination W...
Inverse of a 2x2 Matrix:
• Inverse of a 2x2 Matrix
Inverse of a 3x3 Matrix:
• Inverse of a 3x3 Matrix
__________________________________
Determinant of 2x2 and 3x3 Matrix:
• Determinant of 3x3 Mat...
Determinant of 4x4 Matrix:
• How To Find The Determ...
Cramer's Rule - 2x2 Linear System:
• Cramer's Rule - 2x2 Li...
Cramer's Rule - 3x3 Linear System:
• Cramer's Rule - 3x3 Li...
___________________________________
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Next Video: czcams.com/video/vzt9c7iWPxs/video.html
Final Exams and Video Playlists: www.video-tutor.net/

[@notchildish]

Wow. This is what I failed in high school? Howww? It makes so much sense now. God I wish I could redo high school

[@mnxhsbsbhuh5411]

SomeReallyWeirdGuyLostOnCZcams Lul no u don’t

[@Nitstar6174]

Its never too late to learn!!

[@fonderkieran]

Cry

[@chikamsombanefo4296]

That feeling bro

[@chikamsombanefo4296]

That feeling bro

[@bottleofgreed4415]

A true guide on math subjects. Not like other articles where they just write about weird unreadable equations with no proper explanation.
Watching this really makes us learn it fast.

[@TheAlbaniaGaming]

Hello, just wanted to say i love your videos and they are really helping me with matrices. I noticed that you haven't posted a video about Rank and Range though, i think that you should!

[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you for another solid Linear Algebra video/lecture.

[@Xukkus]

My maths teacher “teaches” us about matrices as if he think we already know it all. He brain dumps everything on the whiteboard and expects us to follow. Some of us just don’t understand it. Someone’s talent with maths isn’t based upon how much they already know, but how well their ability to learn things is, and he just doesn’t give us that opportunity. Thanks for this, really helped.

[@chrissingh98]

yes for real

[@jupiterchris2709]

This is the most incredible and easiest video on solving matrix. Thanks a lot

[@dehanbadenhorst1398]

You make it so easy to comprehend, thanks so much

[@CounterCultureWISE]

Your voice is soothing. Thanks for these!

[@xiaotan2105]

Great instruction. Thank you!

[@chepaulinus2495]

Sir thanks very much for helping not only student's but even people who are not schooling, because you provide just exactly what we want, I wish you where my teacher , because since I started watching your video I eventually become a genius in both mathematics and physics, thanks once more, may God bless you.

[@abugslife2461]

Thank you!! Getting through linear algebra because of you!!

[@among7129]

Just wanna thank you coz really I had missed out on my lecture of matrices it was giving me had time but now I can do it 🙏 .

[@scmane1975]

Thanks it really helped me a lot 😊😊

[@Az__2012]

Why does the scalar matrix turn to positive after multiplying?

[@rootjim1]

Since you start with numbers in the two "example" matrices implies that you're going to tie it into your equation. I'll use your method without the 2 first matrices since you got a positive result. I'm working with augmented matrices, inversion, multiplying matrices etc. I'd like to see your logic since it works. I could resolve the original equation with arithmetic methods but it IS about matrices. Thank you.

[@justdont_peekme7864]

Thank you sir your work is appreciated.

[@HassanYKhan]

Very easily explained. Tumbs for you 👍👍

[@maxwellvukeya731]

THANK YOU SO MUCH, I ACTUALLY FOUND IT HELPFUL....IT HAS ABOLUTELY HELPED ME..

[@maxwellvukeya731]

ABSOLUTELY I MEANT TO SAY..

[@internetcarly]

who else is here because this type of question was on the ACT and you never learned it?

[@mayanksoni214]

Thank you, your videos are helping me a lot.

[@siyakubongafortune5470]

You have always been the best, thank you so much so much ❤️

[@tinashechuchu744]

Great explanation. Thank you.

[@brycentacos]

very help ful video thnaks for your help

[@jatirijhatjhat]

you are saving me. thank you

[@samueldemelash5126]

Best CZcams channel thank you

[@royrolls457]

best teacher ever

[@Saeedalikhann]

this video was very helpful. thanks bro

[@davidayeh1127]

Wow, thank u so much

[@deborah.o.stephen]

God bless you Sir

[@mutintamuchindu5184]

Not exactly what I was looking for but you really are a good teacher, thank you so much.
But am kindly asking how i can solve a metrics problem where by i have a variable in the matrix, for example
A=(1 4) and and B(5 3) then asked to solve for "y"
(3 y)

[@INVALIDZEROTheTitSucker69]

What?

[@danaeclarke3590]

I'm here bc i have a math exam in 4 days and let me say you taught me better than all my math teachers

[@user-jg5id3gw6u]

How was it

[@danaeclarke3590]

@@user-jg5id3gw6u it was mid

[@RKKorou4747]

What if the variable matrix X had a coefficient A which is another given matrix? How will I solve that one?

[@patiencekimz5042]

Thanks bro 😀😀

[@Laura.Kramer]

thanks bro

[@muhanguzidavid1323]

Hey i was watching this video but am asking where did you get this 6A and 4B,??

[@Estoult]

merci

[@nou6197]

what software does he use to draw.

[@anetorjustina6566]

Pls how do you get the number you used for the equation
The 6B and the 2A

[@frankprince5647]

thank u

[@prescottzomb3427]

How about
Given matrix x=(0 -1)
(-3 2)
Find B if x² =B+x

[@bwbs7410]

you only did easy ones. how do u solve for one with a matrix as a coefficient of X

[@frederickbayona5852]

How did the 3 became -3 in the 2B - 3A? Is the operand before the 2nd given Matrix should adapt the operand sign before it?

[@asurgamingsquad8485]

I can help, but you need to pinpoint the exact time of the step you are confused by

[@BoluwatifeElufidipe]

Thank so much ❤❤❤❤

[@loulephille]

Consider Cayley Hamilton Theorem also

[@Jendawy]

why does he switch -2 to + after multiplying by -2

[@lanivelo.lagramalifers3695]

Where did you get the 3A and the 2B?

[@nihatdonmezov8354]

It'll be given to you

[@ayeshajalil5277]

???

[@user-fk8mj6qn9t]

quick question: why is a positive sign left over?

[@rosangapachuau7841]

Sir, one question! Can we just directly write 3A+X=2B as X=2B-3A without substracting 3A+X=2B by 3A?

[@irene991]

Why do we divide by negative 2 at 3:52
?

[@ogoreigns1554]

Thank you, atleast now l can say that l know maths

[@dorafoldesi1475]

Why did you add the two matrices instead of subtracting them in the first example?

[@oyunboldganbaatar7501]

because he already used the negative sign in the equation. it automatically turns it into a plus sign.

[@dorafoldesi1475]

@@oyunboldganbaatar7501 Thanks!

[@faithrichard4342]

@@oyunboldganbaatar7501 thanks i

[@miarayokiy8780]

If i have matA and matB and i have the equation AC-CA=B
How to find the matrices C ?

[@Rohan-et5gf]

It depends upon the order of A and B right??

[@africtv5842]

bro thank you

[@priceymate3386]

3:55 why are you dividing by -2

[@samsam6457]

Where did 3A came from?

[@BonzOmega]

row 1 column 1

[@EasyDaliyEnglish]

It’s part of the given question

[@tres3392]

nakakatuwa kasi wala talaga napasok sa utak ko

[@mavisdom-animeonpiano]

Thanks I didn’t pay attention in class 😂

[@ronymeri4744]

At 1:56 can anyone elaborate why we put a + in front of the matrix ?

[@janieduran2301]

Does it mean that if it's + sign, it should be negative(vice versa) after multiplying?

[@DEATHWISHVQ]

Why did you multiply Matrix B by 2? Where does the 2 come from this wasn’t explained thoroughly for my understanding. Ok we subtract each side by -3A, 3-3A cancels out, cool, 2B - 3A = -1. Ok what happens with the -1? Then suddenly we have to multiply by 2 but why?

[@trisha.gonzales]

how do you find x when it is inside a matrix with a number?

[@hafsaabdi9326]

Even me am searching that the whole day

[@MuhammadbabaMaiwada]

But why is that u convert -2 to positive 3,pls can anyone help me

[@muhamedidrizi6451]

2:00 and 5:00 Can someone explain why does the - sign changes to + sign??

[@EasyDaliyEnglish]

It’s the matrix inverse formula

[@eliottrogers5494]

It’s fucking 3 am and my homework is due 5 hours later

[@Muttisuri]

If you are subtracting 2A throughout the equation to get rid of it on the left side, wouldn't you also need to subtract 2A from X ?

[@Jendawy]

2A - 2A = 0 so its gone

[@mysteryboxxd7897]

Jazakallah

[@tayartsako1006]

why did we divide by negative 2 ? at 3:54 ?

[@KadinWhitney]

Because the x had to be by itself. 2x divided by 2 means dividing everything by two. 👍

[@fayikzhou3755]

I don't know how to get 3A + X = 2B ? 🤔

[@amkai2928]

X= 2B-3A🤦‍♂️

[@EasyDaliyEnglish]

It’s the GIVEN question u get given the A matrix and the B matrix and you solve for X

[@Az__2012]

​@@amkai2928 but why did he then add the matrix?

[@the_burger]

Wow, this is way easier than I thought

[@nimsaramalinthi6343]

My givan equation is 3A + 5B + 2x = 0. It can not devide by 2 in both side to get X. How to get X = ......... From this given formula to solve my prob.. 🚫Plz plz plz help me...

[@EasyDaliyEnglish]

My friend don’t cheat in exam😂

[@Blue_moon1]

I don’t understand how he got 2b

[@shuaebahmed8353]

2b was the part of the given question

[@zy_all]

not me watching this during class -

[@007thematrix007]

@ 0:33

[@Godakuri]

Why are you adding the matrices if the equation states you need to subtract them

[@walterb.7717]

That's what I thought at first, but he multiplies the Marix by the Negative coefficient (-2), therefore, he adds the remaining matrices.

[@rachaeladdo5302]

When he multiply all the elements in the matrix by a negative number, the sign in front is positive.

[@ronymeri4744]

@@rachaeladdo5302 why though

[@MM-np4md]

@@ronymeri4744 I was confused too

[@ZoTrAcK]

I was confused for like 20 minutes also on why multiplying the 2nd matrice by -2 and replacing the formula instead of multplying it by 2 and doing the substraction after regularly.

[@vedadgrozdanic9443]

how would you solve: (AA^T)^-1 * ((B^T * (AA^T))^T

[@ccc-hk6gz]

Ue Ar Veri Quiet

[@FashionforgirlsMehindeandshoes]

Who watching this video in Year 2024

[@wernerxg2064]

✋🙂‍↕️

[@Markus012]

The day before finals 😢

[@tewahmillisha9014]

I to I don't understand

[@user-tu8ep8jq7g]

Please 🙏🥺 can you help me ?

[@Beksvia]

Webale nyo

[@topgamerrajvardhankolape5071]

I am king👑

[@temitayooluwarantimi]

I really don’t understand how 6+[-8]=-2 and 27+[-6]=-21

[@EasyDaliyEnglish]

Simple math😊

[@user-tu8ep8jq7g]

I don't understand 😢😢