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

[@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

[@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

[@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

[@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

[@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

[@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.

[@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

[@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

[@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

[@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.

[@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.

[@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

[@Max47340]

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

[@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

[@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

[@leechaloemtiarana7412]

Who else is here at 1 am struggling?

[@TheoryOfSnek]

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

[@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.

[@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,

[@itoroessien6400]

Discovering this 12 years after, this is a goldmine sir

[@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

[@mhonromopatton8068]

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

[@xiangyucheng-xn4sp]

-1in yellow should be -2

[@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

[@CreativiTimothy]

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

[@CYBERWIZARD]

This is so helpful even though I am in Algebra 2. Having multiple ways to double check myself, even though I can solve a system of equations with 3 variables through substitution and elimination is greatly useful.

[@sledge2742]

way better than any lecturer i've ever had

[@jaredgreathouse3672]

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

[@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.

[@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!

[@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.

[@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 :)

[@LAnonHubbard]

Nice one Sal.

[@IamThatGirlMegan]

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

[@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!

[@jrendoso]

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

[@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

[@fatima60326]

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

[@oazedlium2985]

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

[@mastermix3000]

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

[@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.

[@BerPolo]

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

[@tmgiesen]

You’re a very good teacher. Thank you.

[@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.

[@Killuminatismd]

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

[@kartiksingh_1]

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

[@asianflex786]

@RuudDude1 agreed. if you get bored of an expanation then maths isnt the course for you.

[@klblackstar]

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

[@SakthiPandiSocialMedia]

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

[@CrewNDx]

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

[@Waranle]

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

[@pittsburghguy2520]

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

[@gerardopadilla9934]

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

[@retzuaiga]

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

[@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

[@AmzSongwriter007]

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

[@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

[@-hiandbye1994]

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

[@Eternal-Theory]

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

[@andersonanjo5388]

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

[@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 :)

[@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

[@richardrampersaud6818]

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

[@ludicrouslego2772]

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

[@babybeautified]

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

[@yugi3234]

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

[@ibrahimmuhammad2339]

This was 11 years ago. Still helping people

[@marokay3269]

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

[@bituu_shukla]

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

[@TheRedAzuki]

Programing is very easy to learn if you know math.

[@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

[@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?

[@feitingschatten1]

Just a little extra, there's a free book by Jim Hefferon, who also teaches the cool easy stuff first. It's a good text (as it's free in pdf) to go along

[@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

[@GndmMkv]

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

[@jcp2415]

I hope they were impressed

[@2OthCenturyFox]

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

[@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

[@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

[@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...:)

[@callmehandsomeB_4_24PM]

After 12 years I'm back!

[@poisonpotato1]

It helps a lot in mech engineering

[@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.

[@austinclark6418]

Your voice is so relaxing

[@atorresmusic]

Can one use Matrices to balance chemical equations?

[@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.

[@terencewright2223]

Thank you very much for the excellent video.

[@electricfeel2012]

you are the beast of math!!!

[@Hadas705]

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

[@oOoOoOZabuzaOoOoOo]

Thank you for helping us!

[@veigar1235]

another very valuable explanation.❤

[@GenaEnSamIAm]

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

[@Kennychoco22]

I understood everything except in the end when we don't do anything with the 1/30. i get it when we multiplied the matrices in the end but we didnt with 1/30

[@Bo0meRs0]

8:20 Solving with matrix inverse

[@aku7598]

It's confusing. Ax=b Sometimes A represent Vectors and x the weight as in spaces Sometimes A just scalar with x as vectors as in transformation. Sometimes it's just a way to solve.linear equations.

[@Thiyagadhayalan]

another great video, kudos!