❖ Gaussian Elimination / Gauss-Jordan ❖

[@patrickjmt]

Hi all! Please post comments, questions and anything else on your mind in the comment section! While I try to answer as many questions as I can, there are more questions than I can answer by myself so if you are someone who might be able to help, please do so! The community is so much better when everyone is involved and helping each other out. Our strength is our willingness to help each other! Also please feel free to like or dislike the video. Your feedback is always appreciated so that hopefully I can make my future videos the best possible! Thanks and happy studies!

[@sls6410]

I just watched your video . I appreciate what you do 👍👍

[@jmw1982blue]

Congratulations on 1M subs!!!

[@SaltyBoi420]

Thx dude, your content help me a lot

[@dylanblack8487]

As a student would student have to learn all the method of solving the system of equations to progress in further education?

[@anitepk883]

Thank you very much sir, it really gonna help me in my semester exams

[@DazReht]

The thing i hate most about problems like these is that there are soo many chances to make a stupid arithmetic mistake which in turn will screw up the whole problem.

[@bobdistin9650]

DazReht you can always check the answer with the normal substitution method

[@VroomZOOM]

and you make them half the time or at least I do

[@donlansdonlans3363]

Thats why we use computers

[@kashif2309]

well, i guess that's what you call 'Maths'

[@VndNvwYvvSvv]

@@donlansdonlans3363 Only once you understand how it all works. That's kind of the point here...

[@oseansoldier]

My prof spent 75 minutes and four white boards worth of writing teaching this in class... you did it in a much clearer way in nine minutes.... Thanks for this video! Will definitely help me on the test I am about to take!

[@Move4wrd]

oseansoldier dude tell me about it...

[@abdiqafarhashi8604]

haha, my prof spent months teaching this. and still, we didn't understand.

[@110Turab]

so true

[@nadh3478]

Same.. i dont understand when my teacher teach me.. and .. finally o found this.. its my survivor😋😋

[@YasuoMidOnly]

nadiah abusamah yeah personal vides via yt or whatever is so much better than uni, when will the world change

[@vidpajek]

just saved me 3 hours staring into my class notes, thankyou :D

[@Knowledggge]

same

[@MananFM]

Same

[@joose88k]

😂 same

[@Bek1ris]

Same, qaqam

[@SpaceCowboyTV]

You are a LIFESAVER!! Your videos will be saving the butts of Engineering students for decades hahaha

[@punchtheface]

decades? youtube has only been out for 12 years...

[@westq2]

@PunchTheFace In the upcoming decades lol

[@alanfit99]

*facepalm* just stop lol

[@clintstrong4112]

here 11 months later to chime in and say yes it is!

[@HassaanRaza]

got that right

[@pauljeremyetrata710]

@patrickJMT from my humble beginnings as freshmen engineering student you've been my no. 1 source ,now I'm taking my master's degree your still my source hahahaha

[@patrickjmt]

+Peejay Etrata hahaha, you owe me a beer or 3!

[@clintstrong4112]

glad im not the only one!

[@lennertleysen5777]

engineers see this in their master year? At business school we see this in our freshman year lol

[@JD-jl4yy]

We obviously see this in freshman year as well...

[@shishira.a]

Wait seriously? I saw it in my seventh grade math class and was confused.

[@humanbeing4109]

You and mathpowerisforu got me through calc I , Calc II, calc III and Diff EQ. Its been almost three years since I've taken those classes. I'm finishing my junior year in college (engineering). Here again you are helping me understand something I felt utterly lost in. You have no idea how much you have helped me along my journey . Thank you Patrick for everything you do and continue to do, we who want to continue to grow are very lucky to have you.

[@patrickjmt]

thanks for the kinds words, happy i could help :)

[@TheBaltherion]

You just saved my sorry procrastinator ass.

[@tedjaniaichouche9983]

???

[@alphabetsoup4269]

@@tedjaniaichouche9983 ????????????????????????????????????????????????????????????????????????????????

[@tedjaniaichouche9983]

@@alphabetsoup4269 question ??

[@pulp9058]

​@@tedjaniaichouche9983 *question mark* *question mark* *question mark* *question mark* *question mark* *question mark* *question mark* *question mark* *question mark* *question mark* *question mark*

[@Beaker95]

You have saved my First year of University. Wish I could shake your hand!

[@ahmedtheking123]

hope you are finished by today

[@nayaaccount5575]

Hi where are u

[@erbomba7533]

@@ahmedtheking123 ahahah

[@WolfieTheTallGuy97]

Man thank you so much you officially saved my tomorrow midterm in Maths. Greets from Zadar, Croatia :) .

[@patrickjmt]

+Joseph “Jope” Wolf would love to visit croatia! almost did back in 2011 but went to the canary islands instead :)

[@newkid9807]

Boooo we hate Croatia!!

[@adilmohammed6897]

@@newkid9807 shut up Serbia, nobody cares

[@newkid9807]

@@adilmohammed6897 Serbia #1!!!!!!!!

[@bigrobbyd.6805]

Thank you, sir. My wife is taking college algebra, and the resources and effort put forth by the school are severely lacking. This was an excellent refresher for me, in order that I might teach her better. Again, thank you.

[@xyzoooo401]

thanks man u've been making my study life easier for the last 2 years

[@ThaeSpoop]

Thank you so much! I have an algebra exam soon, and my lecturer cannot for the life of him explain how to do this. Absolute life saver!

[@peaceandlove11-h2b]

omg my uni doctor explained this in 1 hour and half and i didnt understand a word but u made it so simple thank youuu

[@biniyamefrem4816]

Specifically, a matrix is in row echelon form if All nonzero rows (rows with at least one nonzero element) are above any rows of all zeroes (all zero rows, if any, belong at the bottom of the matrix). The leading coefficient (the first nonzero number from the left, also called the pivot) of a nonzero row is always strictly to the right of the leading coefficient of the row above it (some texts add the condition that the leading coefficient must be 1.[1]). All entries in a column below a leading entry are zeroes (implied by the first two criteria).[2]

[@calcinatoir]

Decent explanation, but I had to google around a bit to learn how to do these if the matrix isn't 90% already solved. Should have had less 1's and 0's in the right places at the start and it would have been up to the level and depth of your other work. For instance you don't explain whether you should start by making your diagonal 1's first, or turning the other entries into 0's first. The way you explain it doesn't make it clear. I didn't know you could switch the rows around, or that you could add more than two rows to get your 1's and 0's, etc. Still love your stuff though.

[@beccadragon203]

thank you so much, my lecturer took about an hour to explain this. your explanation is much clearer

[@RaunnHD]

This is amazing! This is entirely brand new to me! I have homework due today but I could not finish the last to problems because of this! Thank you Patrick! Honestly, I wish my professor would tell us certain new solving methods would pop up on my homework instead of having to do it ourselves.

[@AegisOfFreedom]

Good explaination.You may have well saved my semester. Greetings from Greece

[@528morgan]

I just started linear algebra and my professor explained NOTHING. I thought, "I'll watch Khan Academy, so it won't be so confusing." Didn't help. Then, I found your videos. It finally makes sense!!! Thank you so much! :D

[@glizuy1652]

You are truly a blessing. Thanks for helping us thru your video tutorials! ❤

[@patrickjmt]

happy to help!

[@ricardo.mazeto]

I just wasted half an hour with a stupid text book trying to understand it, and you did the job in 8mins. Thanks very much!

[@TheZoeBig]

You, Sir, are a Genius.

[@era2198]

Literally been sitting in class for 3 days not understanding a thing and in 5 minutes your video taught me EVERYTHING.

[@andyh.6021]

When you learn more math from a 10 min vid than 10yrs of school

[@kyyac3596]

I've been struggling to figure this concept out for a week. This video FINALLY made it click! I've finally learned how to complete a problem. Thank you!

[@patrickjmt]

happy i could help you figure it out :)

[@blmiaair]

Seriously, you are a life saver to an engineering student like me haha!! THANK YOU!!!!!!!

[@pearlchoi5734]

Thank you for this video! I've been having a hard time with Gaussian elimination in terms of seeing how everything is rearranged or switched around and whatnot. But seeing it as a single matrix clears everything up!

[@davidthaler7018]

He didn’t use it, but FYI, in Gauss-Jordan elimination, you’d do additional steps to get zeroes ABOVE the main diagonal. That way, you’d see your solution right away (because the coefficient for each variable would be 1) and no back-substitution would be needed.

[@aidstew]

Dude thank you, your channel is so useful. It not only helps me in my classes, but I learn about new things from it. Your awesome

[@codeyhuntting8830]

Dude, your penmanship is AMAZING

[@mantasarul]

Thanks a lot...I usually don't write comment but this time just couldn't resist...I must say you have a good talent in teaching side...keep it up...all the best! Thank You once again...you have no idea how many person you helped via this video!

[@victoriakuhlman9806]

I liked this better than the explanation video on "webassign", where I do all my homework and quizzes. If there is a video for the concept I need made by you, I watch it! They're always good.

[@patrickjmt]

glad you like my videos! email 'webassign' and let them know that you would like to see my content on their site!

[@victoriakuhlman9806]

Hah okay maybe I'll try but I doubt it. They probably have their own instruction staff.

[@michaelladerer8163]

Thank you! I am a math teacher, but haven't done these types of problems in 20 years. This video was a great refresher for me, and made it simple to explain to others.

[@patrickjmt]

glad i could help a fellow teacher :)

[@Mista_G]

And may I add, excellent handwriting

[@Ytremz]

Don't be a kiss-ass lol

[@Mista_G]

Ytremz It's my way of thanking the uploader for teaching me something that my professor failed to teach

[@youcancallmeal7272]

Fantastic video, this is the only one on the entire internet that didn't confuse me. You helped me so much with my test in 2 days, thank you.

[@calebtot]

The sound of a sharpie against printer paper has always made me want to throw myself off a bridge. I can't be the only one.

[@disfordivide]

Lol same i muted this video

[@spiznas]

i actually kind of like the sound....

[@TheBaltherion]

I like the sound. I specifically use sharpie sometimes for it.

[@AlesterPaladin]

It makes me tingle all over. It is a weird sensation while concentrating on this method. lol

[@calebtot]

Alester Paladin Its an ASMR trigger for you. If you've never watched an ASMR video it'll probably be like taking heroin for you since a math tutors video triggers you.

[@LSToralIII]

For almost a week I've been trying to understand this topic being taught in school. Thanks a lot patrick!! Now I understand how gaussian elimination works. :)

[@instaminox]

its seems easy but its anoying not fun at all

[@xenachan3479]

so true,oh I hate exams :'(

[@Kalen1457]

I usually got an incorrect solution because I forgot one stupid negative sign.

[@mohitkarki7185]

That's what maths is all about

[@firstlast2594]

It's kinda like a puzzle ^^ I like.

[@VroomZOOM]

uhh I hate solving these

[@MissA834]

thank you!!!! I've watched so many videos on this and never got it until now! i love you!!!

[@Fanks177]

Very detailed explanation. Thanks!

[@sich254]

in deed you are the best teacher have ever attended his online classes, thanks for you sweeter explanations

[@patrickjmt]

yes, it is interesting! i tell that story as well :)

[@waleedqidan8402]

I want to thank you a whole bunch for these awesome videos. I bought your book (Calculus, 1001 questions for dummies) and it helped me greatly in my final exam!

[@soldiersofmahdi2394]

Thank you so much Sir!!!!!

[@jamesmurillo4857]

from diff calc integral calc and now advance Eng'g math. you always saved someone's life. thank you for the video tutorials.

[@VerryLongName]

I thought you had to get zeros above the diagonal too?

[@11spenso]

+VerryLongName I thought the same ...Im confused

[@Olivia_C_]

+Medaouba Othmane You can, I am not a math person at all but the way my teacher taught it was you get zeros and ones. I wish my teacher would let me plug it in to get the other answers like how the video shows. But there are so many ways to learn this

[@tom_something]

Yesterday I learned Cramer's rule. Wikipedia suggested Gaussian elimination for today's topic. This is the first video I've watched on the topic. It's very straightforward, so thank you. Like Cramer's rule, there's some multiplication involved, but it seems to always be two-factor multiplication, whereas using Cramer's you tend to have as many factors are there are terms in the equations. More room for error and more reliance on the calculator. Also, Cramer's rule feels less intuitive. I don't immediately understand _why_ it works, whereas with Gaussian elimination, it's pretty clear how it comes together. The flipside is, while Cramer's rule seems to rely on more computations, those computations are systematic. You do exactly this, and then exactly that, every problem, every time. Whereas Gaussian elimination does seem to rely on a bit of "creativity". You have to decide how you're going to change the equations to achieve the right result. It's going to vary from one system of equations to another, and I assume also that there a quite a few different choices that will achieve the same end result.

[@Faith-nd2sl]

I have honestly gotten a headache just trying to understand this

[@Keiseth]

I had one hour to figure this out and you made it clear in nine minutes. Much appreciated.

[@KhianVictoryDCalderon]

Does anyone notice he's left handed?

[@4sky]

back during freshman in college i was here. now during my last year I find myself here yet again. i owe you my gratitude

[@photon2724]

ive done the elimination like 50 times and still cant get the 0's and 1's at their rightful positions. When i change one thing, the other thing also changes...........Is there like some sort of steps i could follow to avoid going in a circle......i HATE this so very much

[@Julian-301]

PHOTON when you create a new line\equation in order to change another, ex (r1 x -2) + r2 -> r2 You don’t have to keep the one you make. I now realize how hard this is to explain. Good luck

[@photon2724]

@@Julian-301 haha. did my exam a while ago. luckily it never came up.

[@abhiux360]

where is ELECTRON ?

[@delanimpofu7259]

i'm about to graduate soon. 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. you are special. sending love, light and success from south africa.

[@hoodiehydra7931]

You should work for a collage. your better then my algebra teacher at explaining this stuff

[@bitcoochie4093]

Looks like you need a new English teacher too rofl

[@houstonsisk9380]

bobdabildr12345 well meme'd my friend

[@hoodiehydra7931]

bobdabildr12345 it's a KZbin comment typed from a crappy phone. I'm not sure what you expect.

[@MiguelMartinez-yj7yu]

do you still have that crappy phone?

[@maryannakpama8187]

Thanks for this. Been staring at my books for 2 hours now.

[@GangstaBoiiiiiii]

You sound like Tobias Funke

[@Orteeez]

You're a god, I've learned more from you in the last few hours than i have in my math class during the last few months.

[@henrik123321]

I have no idea what happened but it looks awesome though ;)

[@baileywatson1858]

henrik123321 it’s just a system of letters pretending to be numbers lmao..

[@abdelrahmansaid844]

You are a complete University , I can not imagine how the kind of you doing to all the students in the world and I mean in the world, I am from Egypt and my Uni sucks, but I learn all my math from you.

[@bobbyjones8938]

math the most painful yet fun subject on the green earth...

[@bewanthawijesinghe4266]

so true

[@ericverna1059]

Just got 87% on my exam because of you! The best math teacher online.

[@mayookhin3421]

Please reduce reuse n recycle~ 😊 i couldnt help but notice that you use so much paper to explain

[@mxolisimncwabe3808]

I swear I don't know where I would be without this guy

[@ianopindi8491]

Dude is using easy examples

[@MustangGT-jb6qr]

That’s the idea when introduction a concept. Allow you to master the basic principle and then move on to more difficult applications. Thanks for pointing out the obvious.

[@frondinahishidivali5352]

Thank you so much, my lecturer did not explain very well, thats why it was really hard for me to catch up the topic, but now i feel like iam ready for the exam. You are such a life saver.Loads of blessings .

[@patrickjmt]

You are most welcome

[@itsmako6728]

This literally made no sense

[@lemyul]

o

[@Sunilla789]

This explanation helped me. Thank you for breaking it down into step-by-step. You just saved my mathematics book from being lit on fire.

[@AminiKuarambai-j4v]

Thankyou so much Patrick! This video helps me to understand the Gaussian methods before attending my lectures in class

[@kislaygaurav5596]

bro. i m kislay from india . it's bcoz of u i will pass all my xams.... hats off.. keep loaading bro...

[@wenreaux]

You are the MAN! So sweet and simple. Ready to take on Gaussian Elimination!

[@patrickjmt]

Go forth and conquer!

[@Breakout1211]

MAN I COULDN'T UNDERSTAND ANYTHING IN CLASS YOU SAVED ME THANK YOU

[@sueali4607]

Wooow!! That was so much easier to understand than what my lecturer tried to make me understand! Thanks you!

[@pete2k132]

A in calc 1 and calc 2. Now taking Matrix Algebra. You've been my hero over the years

[@mrjcpenny02]

Finally! someone who can explain. THANK YOU

[@shanehleng185]

Wow thanks for this. You've helped me so many timesssss now. :) Even on your other videos. I just randomly click instructional/tutorial videos that i see (especially the first one that pops out in the long list) and it's only now that i discover that i've been listening to the same person every time i try to search for tutorials in math (ugh i suck in math and you helped me improve that). Also, you have a soothing voice. It helps me focus on your tutorial more :) Thaaaank you, Mr. Patrick(?) :)

[@thomaswiseau2421]

You saved my life mate. Your services are appreciated. Thank you.

[@hurrdurr25]

hi doggy

[@awekeningbro1207]

+hurrdurr25 i want to punch in that freakin face so bad.

[@HazemGhander]

Patrick! You wanna know something? I always recommend your channel to engineering groups of my college,which contain thousands of student. This guy is a phenomenon!

[@nahikoroad]

Lecturer pointed me at your channel. Really helpful for my exams, thx.

[@patrickjmt]

glad you like it and tell the lecturer thanks for recommending my videos as i appreciate it!

[@nataliescarbrough3346]

Thank you so much! I have been trying to figure this out for almost 3 days now and your video finally made it make sense!!

[@ravisha000]

@patrickJMT you are the guardian angel of engineering students

[@kristenthoughts]

I have a midterm coming up on Wednesday. I heard Linear Algebra was easy, but my professor doesn't make it seem as easy. You have GREATLY calmed me down, and after a few more videos, I think I'll tackle the textbook. Thank you. p.s. been here since my Calc 1 TA recommended you last year.

[@andrewsamir1361]

thanks very much man u saved my final exam greets from cairo egypt :) !!!!

[@daymoh5498]

This made it all look so easy. I've rewatched my uni lectures so many times and I just end up phasing out. Glad this was here

[@expidotapologo5999]

this will remain the best video ever watching from the most high institution of learning in BOTS (UNIVERSITY OF BOTSWANA)

[@ibrahimmaki176]

We lack teachers like you, Thank's for your help.

[@karankhajuria2437]

15 mins back I baffled with this "Simple" concept!! Thanks

[@Wolfeywolf16]

Phew! What a math problem! I needed this because I missed this lesson in class.

[@NaoMisweblog]

best maths channel yet!!! keep it coming patrick!

[@stef1790]

Thank you so much, the concept is so easy to understand after this video, yet my professors cannot explain it in a 2 hours lecture...

[@QUALiTYWHORE]

Thanks! Really nice to find someone who can explain it in a good way!

[@shu-tw4fk]

i HAVE A TEST TOMORROW AND YOUI SHOWED ME HOW TO DO THIS IN A SPAN OF 9 MINUTES. THANK YOU

[@funkylly]

You are even better than my university lecturer!!!!! I like u!!

[@georgesadler7830]

Mr. Patrick JMT, thank you for an awesome video on Gaussian Elimination.

[@rishikuntamukala9434]

life saver...A FREAKING LIFE SAVER EVEN AFTER ALL THESE YRS

[@relaxedswede]

Ma dude patrick! You are helping me through engineering school right now! Good looking out man

[@addictingwallflower]

thank you so much Sir. you cleared that up for only nine minutes. thanks again!

[@lukerton5643]

my finite grade might be saved thanks to this video thank you SOOO MUCH

[@belindachen3310]

I watch your videos for my Calculus class, and I was pleasantly surprised to find out that you also have tutorials to help with my Matrix Theory class as well. Thank you for all your help!

[@steffij9775]

When I graduate college you are definitely on my thank you speech