Matrices to solve a system of equations | Matrices | Precalculus | Khan Academy

Using the inverse of a matrix to solve a system of equations.
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[@pranavsood2058]

"I hope i'm not boring you". Me: No Sal, you are amazing you are helping me with my exam

[@adramalech5109]

Pranav Sood I would've liked your comment but it has 69 likes

[@ashishkumarsharma1323]

tejas joshi 109!

[@jjune2653]

Ashish Kumar Sharma 188 likes!

[@mangacartoonandsong4740]

Pranav Sood good

[@mangacartoonandsong4740]

Berk Can Yazılı haa

[@MWSART]

beyond everything you got a great voice sir..soothes the ear

[@loneranger7831]

This video is 15 years old, and it is still super helpful.

[@Twaj_]

pythagoras was born 2594 years ago and his theorem is still helpful, math is cool like that

[@natassciabryce2946]

Thank God i found you cuz my math teacher messed me the hell up

[@LizbethAyala]

NATASSCIA BRYCE 😂

[@monstercl1668]

NATASSCIA BRYCE

[@duck8024]

Same here

[@random_scum]

I feel you, bro.

[@theodrinksman4119]

Tbh i learn more by watching this 16mins. Video than my teacher explaining it for 2 hours

[@metalheadlass]

When I watch these videos, I really start to wonder why my teacher gets paid. This guy is doing a service to humanity by doing this, honestly. Wouldn't be here if my teacher was worth anything, so thanks for the real education.

[@lakshyasoni7696]

Yeah, teachers are trash

[@joeytrevino2903]

I have an exam in 2 days and my professor basically relies on us learning from the book and not him teaching us. I have to get to video number 47 in this wonderful playlist. I am currently on video 7 and I have already learned things that I didn't know I needed to learn. Thank you for this collection.

[@travisc8406]

lmao a bit late but how did it go?

[@jozie892]

@@travisc8406 if I remember correctly this was my precal class and I passed. Also graduated but thanks. Video was helpful.

[@TheReck12]

My teacher skipped matrices in algebra 2 so here I am in pre calc and I have no idea what any of this is

[@brucexu313]

nah it's ok I'm in IB HL and have no idea what any of this is

[@xx-sg8wx]

I never learned matrices until the end of AP Calculus BC lol

[@ghostofmisao.]

I'm in Algebra 2 rn and I don't understand this stuff 😂

[@omariqbalhamid280]

Matrix starts in precalc

[@harleighstringer]

ive taken literally precal, cal 1,2, and 3 and don't remember ever doing these. now im in linear algebra struggling and beyond confused

[@roninovereasy]

Matrices are the fundamental building blocks for building models. This is utilized in several aspects of data science including machine learning, statistics including regressions. And conceptually, it is hard. Anyone who thinks they are stupid are wrong (otherwise you wouldn't be watching these videos in the first place). Just keep plugging.

[@IngaMitinyan]

+Fred Sanchious thanks for the encouragement!

[@andrewmunnings4545]

Fred Sanchious thanks for the encouragement

[@metallisac]

Or people are learning this in the first place because they simply have homework. Fuck math lol

[@brooke4603]

i needed this

[@aku7598]

It's confusing. Ax=b Sometimes A represent Vectors and x the weight. Sometimes A just scalar with x as a vector.

[@dannapolitano9616]

matrix = bullet to my brain

[@jordanpayne8826]

This video literally couldve been two minutes but i still love you

[@GeForce1080]

2008: Nope 2098: Nope 2010: Nope 2011: Nope 2012: Nope 2013: Nope 2014: Nope 2015: Nope 2016: Nope 2017: Nope 2018: Nope 2019:* Now is the time!!*

[@skrumb]

2098 been a rough year

[@ethanstone2197]

DANOS time travel

[@TheDerpyCornDog]

*2020

[@kiwi-sk3eo]

2020 dude

[@shreykakkar4810]

2098 should be a good year

[@Starchildcasanova]

I don't see how anyone could dislike this video. I want you to know that this refresher is going to help me pass Mechanics class. Thank you.

[@jg6551]

he starts solving with matrices at 12:00 if you are here for a quick review go to 12:00

[@DrawingHeart]

JWG Fishies thanks dude

[@jagdishkarelia3648]

U saved my time!!!! 😱

[@Spartans-community]

Thanks man

[@Yass-um5kz]

thanks 🙏🙏

[@Nicklenenners]

THANK YOU SO MYCH OMGGGG

[@hypercube3495]

Khan academy is so legendary I was 3 years old when this video was published. I watched these in 5th grade I watched these in high school and now I’m watching these while taking calculus in college. It’s totally tripping me out that this video has been ready and waiting since around the time I learned to count to teach math in a way I understand thanks khan.

[@DrawingHeart]

Anyone else hopelessly lost

[@yeabsraamare6615]

if this video is a bit confusing then you should join the channel " The Organic chemistry tutor" that dude is amazing like A++++

[@ServitorSkull]

Fear not friend. As long as there is math, we have hope.

[@rrrr-ij4zc]

43 years old and understanding this just now. What did I 'learn' in high school math and in math that I had in 1st year of university? Something like Sal's video would have save me a lot of trouble. Maybe I should feel grateful that I am understanding this at least now.

[@TheAutumnWinter]

Thanks so much! I got behind in class and failed a quiz yesterday on this subject. I have a test tomorrow on matrices and now I'm not worried about failing it! I'm a tactual learner, so being able to use steps makes it so much easier for me! You're a lifesaver!

[@016abhirajpal9]

hey how are you today ? and how did your test go ?

[@RohitKUMAR-np8qd]

what are u doing now

[@OrthosWasTaken]

My guy, you've probably got comments like these thousands of times but I'm on a fast track math class as I could never get my GCSE, as I found math to hard. But you for whatever reason are so intuitive to follow. Thank you for being one of the major reasons I'm going to university,

[@Max47340]

I usually enjoy your videos, but on this one you bombed! I’m more confused than before 😮

[@MSFR-911_]

سبحان الله وبحمده سبحان الله العظيم استغفر الله العظيم الذي لا إله إلا هو الحي القيوم و أتوب إليه سبحان الله وبحمده عدد خلقه ورضا نفسه وزنة عرشه ومداد كلماته اللهم صَلِّ وسَلّمْ عَلَى نَبِيْنَا مُحَمد ﷺ

[@leechaloemtiarana7412]

Who else is here at 1 am struggling?

[@TheoryOfSnek]

11:37 for me as I’m typing this, but close enough

[@andrewogden1480]

Khan, I love you! I have been sitting in class for 2 weeks now and have never been more confused. Your videos always start off so basic that you can pick up any where in a subject.

[@indistantdreams]

old gold days. 240p videos. memories.

[@marcusantonius4121]

At my school we also have to use matrices to solve equations that simplify down to 0=0 i.e. 2x+y=2 4x+2y=4

[@alyssabalabanova1918]

Thank you so, so, so much for these videos! I am doing a Masters degree and had to understand matrices for the underlying equations in statistics and if it was not for your videos, I might have given up! Thank you, you are amazing :)

[@anjalipal3031]

i’m in calc and i’d NEVER even heard of these until i was taking the pre-ACT a few weeks ago... thank god for khan academy

[@itoroessien6400]

Discovering this 12 years after, this is a goldmine sir

[@jrendoso]

such a wonderful video, really helpful. i wonder how to do this whit a 3x3 or 4x4 matrix.

[@SoloPro]

It was a very nice video and I have learnt a lot in 1hour... I will probs try watch all of the playlist because its so easy to follow... Thanks sal

[@jaredgreathouse3672]

I now can really USE matrices in statistical applications, namely in regression analysis, command writing for Stata and for solving systems of equations

[@mhonromopatton8068]

Love how you can't stop thinking about The Matrix Movie while doing matrices..............Thanks alot for this free and valuable education SAL💖💖

[@rinnegansr5980]

"so this is stuff you should already know so well skip this" thanks maths professor even in the advanced books that super nerds used i couldnt find it.

[@jiyoonpark5022]

11 years have passed and still, there is no video that exceeds this one

[@jacob240694]

Switching from an Architecture degree to aerospace engineering - these videos are making my life so much easier! Thanks!

[@CreativiTimothy]

His handwriting really improved 10 years later lol. He wrote his -2 as -1 and his 3 as 2 at 14:28

[@ludicrouslego2772]

Omg this makes way more sense now! Thank you now I’m fully prepared for the test I’m taking soon.

[@richardrampersaud6818]

Thank you so much for this, it's so much clearer now!

[@sledge2742]

way better than any lecturer i've ever had

[@muntynz]

Love it, you are a fantastic teacher, no mono tone and you answer ALL my questions... Thank you for taking the time.

[@RohitKUMAR-np8qd]

@@heartcomedy5 hoping he's doing great

[@SakthiPandiSocialMedia]

This really helped me for my math test! Thanks Sal!

[@fatima60326]

I didnt get the visual represenation amd explaination of it despite the others in matrix series of video which was amazing so far

[@IamThatGirlMegan]

you explain this better than anyone who has tried to teach me. Going to ace my test tomorrow!

[@tmgiesen]

You’re a very good teacher. Thank you.

[@BerPolo]

Very nice tutorial. Definitely helps, teacher doesn't explain much.

[@FelipeZucchetti]

Thanks Sal for your fucking awesome explanations...i hope one day to be able and pay you back for all free knowledge you share...I really appreciate your videos...already watched almost all calculus videos and now im starting linear algebra...you are a great teacher...thanks again...:)

[@MSFR-911_]

ورد عن رسول الله ﷺ: اللهم أنت ربي لا إله إلا أنت، خلقتني وأنا عبدك، وأنا على عهدك ووعدك ما استطعت، أعوذ بك من شر ما صنعت، أبوء لك بنعمتك علي، وأبوء بذنبي فاغفر لي فإنه لا يغفر الذنوب إلا أنت، من قالها حين يمسي فمات من ليلته دخل الجنة، ومن قالها حين يصبح فمات من يومه دخل الجنة

[@kartiksingh_1]

I want a world in which every teacher explains like you do

[@jeffgalef121]

Thank you so much for explaining the intuition behind this. I always found it shocking that you could find a vector that satisfies multiple equations, but your drawing of the intersection of lines made this very clear.

[@darksteel78]

The only thing I can say is thank God my teacher taught me Cramer's Rule. I find it to be way simpler. You should make a video on it Sal if you haven't already. This method also gets the job done though.

[@KlaskeyProductions]

This makes much more sense than the way my linear algebra professor taught it. This method of "examples now, prove later" works much better than its inverse, IMO. Maybe it's just me though.

[@arbbra6837]

What does the ethics mean to you? This guy (Sal) has shared more than 3500 tutorials with no charge, I consider this as a high human value! By the way I think that today Sal is the synonim of the humanity and academism together!

[@mastermix3000]

THANK YOU!!!!!!!!!! I SWEAR some people are just much better than teachers

[@barbellbrat]

I have two more days till school starts, and a packet that I have to get at least B- to be accepted into AP Algebra II. I know everything in the packet, but guess what I don't know? Matrices, I spent literally 2 hours trying to figure out how to do this crap that I've never learned, and trying to learn it from 20 minutes of bullshit. Thank you.

[@Alhussainba]

how did you do with the school ?

[@jasonwalker6285]

How'd it go where you at now fam

[@andywattanaskolpant8378]

How'd it go?

[@justsomeguy7921]

Don’t want to be repetitive of everyone else, but how did it go, and how are you doing now?

[@andersonanjo5388]

lately your math calculations have been helping me alot. Thank you very much Sir.

[@LAnonHubbard]

Nice one Sal.

[@youneedlenny6542]

Yeet I have a math final tomorrow and I don’t know what I’m doing

[@CristianGarcia-vd1it]

Same fam just that mine is tomorrow

[@anupsharma8547]

You are Brave

[@retzuaiga]

this refresh my memory, i need this for higher level courses

[@nightwolfz]

Thanks for the videos!!! You're a life saver!! P.S. You could use windows journal, everything you write will look much cooler because of anti-aliasing, just change the paper color to black and disable vertical lines/margin.

[@gamingverse8181]

wow 12 years later and still helps

[@Waranle]

Thank you alot Khan. Im going to take linear Algebra this fall.

[@CrewNDx]

Thanks for making me love maths without asking for even a single penny. you deserve the best in the world. Sal 💙

[@Eternal-Theory]

My homeschool book does a crappy job explaining any of these. Thank you for the help!

[@evalynns8530]

Thank you so much!!! The way my teacher described it had me so confused, but this makes so much more sense, and it's way faster! :D

[@gerardopadilla9934]

About to take my final in like 30 minutes this gonna help so much

[@PepperAddict]

Yes we all should have learned how to solve linear equations in middle school but now we are using linear equations as an example to learn how matrices are used to find the solution for hundreds of linear equations

[@tarakenabay6384]

This is beautiful! Thank you

[@bituu_shukla]

Hello sir I'm watching your lectures ,from India ❤

[@-hiandbye1994]

This is more helpful than my teacher trying to teach using Matrices to solve a system of equations.

[@marokay3269]

yay!!! now I can do my assignment....my brain was dead coz of not doing matrices in so long...its coming back to life. thank-you :)

[@klblackstar]

yes, there is. both of those methods will work.

[@terencewright2223]

Thank you very much for the excellent video.

[@xiangyucheng-xn4sp]

-1in yellow should be -2

[@pittsburghguy2520]

You actually made this harder than it already was, wow thats a first

[@2OthCenturyFox]

Thanks for the info, however you need to get some new software!

[@GndmMkv]

im going to show this in my class and amaze my teacher

[@jcp2415]

I hope they were impressed

[@oOoOoOZabuzaOoOoOo]

Thank you for helping us!

[@Thiyagadhayalan]

another great video, kudos!

[@Killuminatismd]

so proud to be a bengali. I look up to this man. We need men like him to further humanity :)

[@a00000z100]

I'm wondering about why did you add ( 6*7 ) + ( 2*6 ) at 15:06 . Why you did not subtract as the first one

[@indiaparker3719]

his hand writing was bad so its actually (6*7) + (3*6) but you are right he subtracted the first one which was (6*7) and (2*6) and he got thirty. i was super confused because i have not seen him do it that way so i think its a mistake.

[@veigar1235]

another very valuable explanation.❤

[@Hadas705]

Thanks so much, I can't understand my professor and Khan academy explained it very well

[@GenaEnSamIAm]

Couldn't agree more!!!! Nicely put!

[@TJJ727]

Thank you! Very helpful

[@lancelindlelee7256]

Thanks. Another time this is useful is when you are allowed to use a calculator. My calc can do a 4x4 matrix but only 3 systems of equations

[@yugi3234]

THANK YOU SO MUCH Awesome video my math teacher at school explained this horribly thank you for clearing it all up for me

[@bgpeters22]

I've read that it's not great practice to use the terms inverse and reciprocal interchangeably due to them having different meanings in calculus. For example (f^-1(x)) is not equal to 1/f(x).

[@joshuacole4037]

Pokemans

[@oazedlium2985]

2:26 y= -3/2.x +7/2

[@poisonpotato1]

It helps a lot in mech engineering

[@HiHi-vv2yn]

can get the 2 lines(not sure what they are called) from that intersect point found via matrix?

[@AmzSongwriter007]

rearrange it so it looks like -x + y = 4, then you can do the problem this way.

[@electricfeel2012]

you are the beast of math!!!

[@austinclark6418]

Your voice is so relaxing

[@Johan-st4rv]

I am in Calculus III and found this to be quite complicated no idea how I managed to get it all the way back in Precalculus

[@babybeautified]

See this is how young ppl in this generation can learn effectively.

[@friskkyy21]

i love this guy man!.... God bless you khan :D

[@jonhall2698]

Your a life saver

[@atorresmusic]

How do you solve a 6x6 matrix? or for that matter an nxn matrix?

[@ibrahimmuhammad2339]

This was 11 years ago. Still helping people

[@duwaynesmith2602]

can u do a videos on matrix equations not requiring inverses

[@azimebrahimi]

beautifully explained

[@marokay3269]

your such a khan academy student :D "some people learn at different paces"