❖ The Span of a Set of Vectors ❖

[@patrickjmt]

Hi all! Please post comments, questions and anything else on your mind in the comment section! Also, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly as it helps me :)

[@lisro21]

You don't know how many times you have saved my ass from going to McDonalds to apply for a job

[@iLoveTurtlesHaha]

LMAO.

[@ajeet3259]

Where are u now?

[@chloetzpiano6548]

So you work in kfc now?

[@ahmadyogi1340]

@@chloetzpiano6548 No, he's doing fine(I hope)

[@normanhenderson7300]

There are intelligent and mathematical people who happens to work at McDonal.

[@patrickjmt]

awesome, i am glad my boring videos could somehow help you want to pursue math! and my advice: pair up the math degree with something applied like CS, engineering, economics, etc.. unless you are wanting to be a math teacher or prof. i think jobs are hard to come by with only a pure math undergrad.

[@CalmThrill]

Taught me more in the first 2 minutes than my Linear Algebra professor does in an hour.

[@friendsclips8141]

I Agree

[@isabellapardo244]

Same

[@alanmozo3659]

Same, now with the online semester it’s more easy to see short videos than a class of three hours

[@dushandilshika7389]

Absolutely 🤓

[@divykanani4551]

Totally agreed

[@stiner2829]

Ha well for four years now (since I started calc 1) I've been watching your vids. Now this is my last math class and I'm still here! Thanks for all the help man

[@narutouchiha1946]

math major?

[@jordanwinter3190]

This math is too easy for it to be last class of a math major.

[@kucingyangbasah]

Stiner282 SAME!!!

[@scottsliftedxj]

@@jordanwinter3190 it's my last math class for a math minor. Calc 1-3 diff eq and linear

[@scottsliftedxj]

But I agree with you I'm not arguing your statement

[@Sam-db8gv]

YOU JUST SAVED MY WHOLE SEMESTER AND GAVE ME HOPE AND LOVE FOR MATH. MANY THANKS!

[@shyger778]

me doing my bachelor's in engineering in 2k23, watching this 11 y/o piece of masterpiece thanking you heartfully sir 🙂✌🏼

[@stevenan93]

PATRICK U DA REAL MVP

[@Flowerlifts111]

k

[@SpaceJesus25]

so random im dyin

[@vielleichtspater5484]

English is not even my first language but this guy just says 3 sentences and all my problems of the last 2 days are gone xD

[@burlapse4113]

You explained this 100000000x better than my teacher, GOOD JOB!

[@delanimpofu7259]

i'm about to graduate and i'm considering doing my honours with a mathematics major. i cannot thank you enough for all the content you post and understanding you bring. my enjoyment of mathematics is largely because of you. you are special. sending love, light and success. from south africa.

[@VerdictVerdictaon798]

You are a good math tutor. God brought you on earth to save some of us from hard University and College Maths concepts and He is gladly proud of you

[@patrickjmt]

God wants you to go to 'patreon' and help support my math video creations as well

[@nvlfs1995]

patrick sacrifices his time for us youtubers for our maths and you cannot sacrifice some little donation. you can donate what you can, and when you have job , you should donate more.

[@KidCudi72]

How is he an asshole for saying he's going to donate when he has the means to? He's already putting money in Patrick's pocket by watching the video and commenting.

[@pranjalbhatt8862]

Bash Barti bcoz he never monetizes his videos.

[@EssentialYachting]

CHRISTIAN ZIKPI lol im in 10th grade

[@Thedude5007]

You Sir are a legend, I cannot begin to count the number of times you saved me, thank you very much. :)

[@jjoben459]

Thank you for actually writing out the problems. My professor tends to skip this over and focus more on proofs, and most of the kids in my class are math geniuses and whisper under their breath about me when I ask questions.

[@patrickjmt]

glad i could help you out :)

[@MrArekusa]

You, sir, are amazing. I don't know why all teachers don't teach like you do, the world would be just that bit more smart and probably so much more passionate about mathematics if they did.

[@salmanmuhammad8159]

Dont ever stop making video . you got talent man.

[@sonaligautam4081]

You are the BEST math teacher. You make it so easy to understand. Thank You.

[@danooii]

You've been my guide for the last 3 years, since the beginning of precalculus, through all of calculus, diff equations, and now linear algebra, the last math class I'll ever need in my major. Thank you!

[@rickywiggins7861]

PatrickJMT may you live a long prosperous good sir because you have saved mine : )

[@garyfoo8821]

Best teacher. Practical and simple to understand. Thank you.

[@SN-dy2jr]

I have been watching your videos since high school, 4 yrs ago.. and they inspired me to study maths for my degree, and i am rocking with A-pluses, just because of your help. i guess it is the time to thank you more.. You are the best

[@planetscizor]

why bother going to class when Patrick teaches you so well. Teachers needs to go ask him on how to teach!

[@flawns]

Because he doesn't cover ALL the information in linear algebra...

[@planetscizor]

i passed my class following him, did not attend a single lecture after the first 2.

[@flawns]

You must have had a easy-to-fair professor. Our class has 0 calculations, only proofs :|

[@planetscizor]

I guess its a matter of understanding the material. Don't get me wrong, I just didn't watch his video and call it a day. I did almost all the problems in my book so grasp the materials. After all practice makes perfection.

[@lordreyna6924]

Planet Scizor this is why I take my math classes online it’s not like the teachers actually help. I swear robots would be more efficient and effective than what the education deems sufficient in producing over inflated egotistical professors that just follow a read and speak objective book all teachers get.

[@samg]

finished calc 2 and your videos were very helpful. Start searching for linear algebra study and you're here again. bless you

[@GY9944]

I gotta say,I understood from your relatively shorter videos more than what I understood from longer boring MIT lectures.You're great,thanks.

[@99ludester]

I swear, I only have to listen for about 3 minutes of your explanations and I can find most of my errors. You are awesome sir.

[@Benjofresh]

I cannot even describe how in debt I am to you, Patrick. You are the sole reason I have an A in Calculus II at Ga Tech. Thank you for filling the world with more awesome!

[@Thejessica-silva]

Don't think I would have made it to linear alg/diff eq without your tutorials, haha. Awesome job!

[@patrickjmt]

glad i could help!

[@PENDANTturnips]

bae

[@higgsbp139]

Couldn't help but smile when I watched this video. This concept had me stymied for weeks and within 1 minute of your video it made perfect sense.

[@AwookieGaming1]

This channel saved me from horrid professors at poorly run research universities where zero fudges are given about teaching.

[@Haidar-Salam-92]

You're So Sweet Yar You Ta Taught Me Those Concept In Just Only 10 Minutes Which Concept We Doesn't Learn From A Professor In Six Months.

[@Acesif]

Amazing video dude. Explained it better in 17 mins compared to an entire class by my university teacher

[@zachmichael3153]

My teacher sucked at explaining this to us. He couldn't even answer basic questions but you made it so easy to understand. Thank you!!!

[@patrickjmt]

my pleasure!

[@vestabeats6007]

One that actually talks about the formula and gives examples. THANKS!

[@andredagold5561]

You, patrickJMT, are the real MVP. (Mathematically Valued Person XD). Thank you for your videos!!

[@christinestraub7242]

You are the best. I always brag about you to my classmates! I learned most of my calculus and other math with your tutorials. I hope you are doing physics too and life would be so much easier! :D

[@kyrinky]

If he does not do physics, check out AKlectures, amazing tutor.

[@markmicronet]

I got stuck learning the about span of a set of vectors. And this is the only video that I stumbled upon that explained the concept so EASILY....

[@adrenalinerush369]

Hi Mr.Patrick! I would just like to thank you for taking the time to do these video tutorials. I lacked the confidence in doing math before but thanks to your easy to follow tutorials, I have been able to do well in my math-related classes. Thank you!

[@andrewdeuriarte9147]

Thank you so much, was very confused about this topic and now have a general understanding!!

[@daisyflat]

Big mental hugs to you, good sir!

[@simmonstrumpet]

Loved the part where in his head he did -92*3, then stumbles on -276+280. Amazingly helpful video, just made me laugh. Just like on tests, I'll do an amazingly long problem, and miss an addition/subtraction.

[@jatoday]

YOU ARE THE MATHS MESSIAH! Thanks. You're the best!

[@3zombie81]

yes you are my real prof, now i can focus on solving problems.

[@DreamDaze777]

Me preparing for exam watching this 11 year old vidoes😅😅

[@oshinjasper9911]

12yrs now

[@ajayidemilade2113]

Same here lmao, OAU😪

[@forall0784]

13 years now

[@MRUZAINI]

the way you solve the equations is brilliant!

[@אוריפרץ-ח9ב]

i just watch this all video without sound and still understood everything, you are amazing

[@williamreyes3801]

Better than my linear algebra teacher. Thank you Institution of Patrick JMT

[@patrickjmt]

@billtruttschel thanks! i added an annotation about it; hopefully people will notice it.

[@kinggiroud8233]

dude u explain this better than my textbooks and lecturer combined

[@qusaialmasri3349]

literally saved my life bro, you're amazing...

[@JOHNKIMANIKym]

My lecturer has a rather convoluted way of introducing very simple concepts. I have watched this video and comparing the approach with that of my prof., I think my prof needs some training on demystifying the learning of mathematics. Keep it up Patrick. I love the work you're doing. God bless you.

[@rachelwiggy]

Thank you SO much for taking the time to do this!! This topic makes so much more sense!

[@thatgenesis27]

i am surviving math subjects because of you sir! you ! you rock!

[@palvindarchhokar9821]

Dude! These videos are awesome, blew my mind! Thanks!

[@jy9255]

Take my money man this is epic

[@kyuss0x1]

God bless you ! i was struggling with algebra until 1 min ago i watched this video :) you R-O-C-K !

[@victorialewis6084]

Your videos are fabulous. I tell all my students to look for your explanation online. Thanks for the valuable extra resource

[@footprints2006]

You make my linear algebra textbook make so much more sense ty

[@cho.gath789]

I like your teaching style with covering different parts with the pieces of paper, and revealing it step by step.

[@yashwishah3408]

wow never knew this was uploded 12 years back thank youu sirr!!!

[@davidontiveroz8295]

You are doing the lord's work my sweet lovely patrickjmt

[@idrisadesina4962]

Patrick, you are the realest nigguh out there

[@iLoveTurtlesHaha]

YES!!! Thank patrick for having a linear algebra section. Last semester you helped with Calculus, this semester it's LA. You're da man. I love this guy. XD

[@scubadorge]

Thank you for showing very single step. Visual learners everywhere appreciate it. 👍🏼

[@devdayz101]

I just wanted to come back here and thank you fam. Looked like I was going to fail linear algebra this year but then I found your videos before my final and ended up passing the course. All thanks to you!

[@patrickjmt]

congrats!

[@tutiha]

I just love you! You make this video right before I need to revise linear algebra. How come you are just right on time :))))

[@sreekeshv12]

Thanks Patrick you saved me for tomorrow's exam

[@zeeshan3dge]

I think Patrick knows which subject tutorials I need when I was studying Calculus I he made lots of tutorial of Calculus I now I need in Linear Algebra.:D Thanks a lot...

[@mathyouforgot]

You have no idea how badly you just helped me.

[@jacobfontaine216]

thank you man, i appriciate all the work you put in. Wouldn't were i am rn without it

[@patrickjmt]

glad that you like them :)

[@fakecrime]

Your videos always rekindle my love for Math. Thank you!

[@mcguire700]

I've been using your videos to help me since calc I through diff e.q. and now linear algebra lol, they have been invaluable to me, thanks for the videos!

[@cangurel7917]

this... this saved my ass big time, thanks man. awesome work

[@patrickjmt]

+Can GÜREL happy i could help!

[@cohi27]

All of your vids are great bro, thanks a million.

[@ariellalee4749]

Great video, extremely helpful. Your tutorials are always so clear! Thank you so much.

[@stephenn5920]

You my friend are a genius, and a very helpful man. You just took me a step closer to be an engineer

[@jonathanmukwaya6870]

Thank You Patrick you will be blessed for this God willing.

[@nickmuntzing5135]

Dude... (exhales relief) Thank You

[@patrickjmt]

@tutiha well, a few people told me i am a semester too late! : )

[@metal4bld]

this stuff isnt that hard but my god is it a boring subject

[@gingerbredm4n]

honestly when patrick or khan academy explains this stuff its very easy to me but my professor absolutely blows at explaining any of this

[@RequiemForABuckeye]

Alex Gieleghem same

[@Thadnill]

I agree, it's not that complicated but it's so boring that it makes me want to puke... Which makes it hard because i can't stay focused haha, Luckily we at least have patrick...

[@HK-sw3vi]

have you taken probability and statistics?

[@doubitn7969]

Alex Gieleghem Same, all that I could hear from my professor was” Zhis, ando zhis. Yeah and Nowuu~ We move to zhe next.”

[@dhimanroy1671]

You really help me to clear my concept.

[@NexFuturex]

I want to just tell about you " your are on the perfect way and you have to go on".Thanks and Thanks.

[@nabeelnaeem6323]

Thank you sir Such and easy method you are using and I am understanding it very well

[@galgalodida2783]

you really made linear algebra simple,thank alot for this great tutorial

[@patrickjmt]

You're very welcome!

[@erikrameaux1360]

amazed with linear algebra by the way you explain and illustrate by example. thank you sir!

[@joelloh3633]

Thanks man, Linear Algebra finally makes sense!!!!

[@MrAlbashiri]

Thank you very very much. Your videos helped me a lot. I don't know what would I do without your videos. =D BIG THANKS =D

[@rochranomajeccavea]

Hi Pat! I'm taking Applied Mathematics and you're doing great!!

[@TheUnorganizedBaker]

You sir, saved my life! I not only understood I actually learned! Thank you! :)

[@bu3b00d]

I love you Patrick!

[@ceeejh]

The videos are not arranged properly. I want to know what video is before this one? Better yet, can you post a list of how I should watch this playlist. I love your videos though. They are to the point and simple. Thank you Patrick, you're the real deal!

[@byron0324]

your video help me a lot from macao, china.

[@cerenalir5032]

you are my savior . Thank god ! Man you must be awarded ( please start lecturing in our university :D)

[@touraya]

Thank you for your awesome videos!! I really wonder what I'd do without you..!!

[@mohamedamin2232]

thank you very much , you make me happy ,, keep going , Thank you .

[@blueghost00]

What I like about your videos is your voice. To me at least, you sound young, which makes it feel like I'm learning this from one of my friends. That, and you know what the hell you're talking about. Thanks for your help.

[@amyspeers839]

Thank you so much this was incredibly helpful.

[@natashaparrott8593]

You might be my only hope at passing my first year at uni

[@alienmoondudes8071]

thank you for making this video!!! it. has TRUELY helped me understand the concept of spanning