Solving 3 Equations with 3 Unknowns

[chechennyboiiy]

dont have to go to math classes anymore, woohoo

[deathmeizter]

thank you

[mosaviadel]

Awesome

So easy way

Thanks

[DemonikOu]

Whoever is further interested I suggest GeoGebra 5 which is free and it supports 3D modeling! You just have type the equations and it's ready ^^.

[TVDDC]

actually 6:00 the method is called the method of Gauss-Jordan

[TVDDC]

I'm studying mathematic 8h a week - science and those vids are a realy help! we have about 6 books for maths but you don't learn a shit out of it. thanks to khan because they'll be my futur!

[Forcomputerclass2]

My teacher gives us extra credit to watch these videos! :)

[whitetigerpals]

"I'm just writing it in a form that has a little bit less...letters in it." lol, this guy is great.

[Robubbabub]

@h0minid25

Why are you even taking the class then? Education is a complete waste of time/money if it isn't applied into your job/life. Unless you're in highschool, then it's not as bad.

[shannonz92]

how did you get the 4 in (-x+6+4 = 9)? isnt the 4 suppose to be a 2....

[h0minid25]

The only reason I'm hear is to pass class. Not to help in my life.

[siuavaka1]

lmao 2:14--->, 10-0 is ten....wea did this guy get his zero from lol

[Quasrelsanct]

My matrix is augmented

[epicshrimpgerald]

wow you really like your colors

[Dragongod41]

2:13 I believe y=0 not 10 :)

[zryda07]

what about the elementary row operations? I never saw you interchange rows or explain those laws.

[sfkc1588]

@zryda07 There are 3 EROs:

1. You can add a multiple of a row to another row.

2. You can mulitply a row by a non-zero constant.

3. You can interchange two rows.

[zainahmed1994]

/watch?v=AsbYLQJDaK8

watch this video.. its in some different language but has used a 3d software to represent intersection of 3 planes.. it will give you a intuition of it in a less messier way..

[Banjo597]

Try figuring out a matrix equation on how to have dinner with your wife

[donogam]

When my teacher explained it, i didnt understand much. But this vid helped me a lot. Thx, your doing a great job. Just wanted you to know that we appreciate your work here in Norway aswell.

[MsCanCan08]

he kinda confused me with matrices.... 

[liljunior805]

this shit is hard

[VHSBD]

Just used this to help me solve an electrical engineering problem for uni. Hurrah for Khan!

[pentakillace]

@VHSBD Bro this is Grade 10 math lmfao.

[CravenFireX]

@pentakillace You're obviously not in university. This is also used in first year linear algebra. It's used for solving matrices and what not.

[mrmkowals2]

@pentakillace wanna know something crazy, bro?! i still ADD and SUBSTRACT in 4th year math! :O that's like kindergarten math ROFL

[chuckabuckmoore]

Great job, but the solution set is (-1,3,-2).

[milosivanovic1]

You are simply amazing! I value your work to the extreme Sal!

[Kinghercules]

LOL!!

I did do some of these over the weekend just for kicks.

:-)

[juaneco1980]

Can't do anything without some room to work with.

[lizwilder]

Thankyou sooo much , you have really made a difference to my studies.

[46DOCvr]

Great

[dnanetwork]

This might help kids and good job sir :-)

[eagleduzt]

Mr Khan: "My wife is downstairs, im supposed to go eat out".

...Interesting

[juaneco1980]

@eagleduzt Unlike many of us, he talks his mind, which make these videos so great.

[trekgeek1]

The only thing I don't like is that you put the simultaneous equations into a matrix, reduced the matrix, and then put the reduced matrix back into simultaneous equations to solve. You could have just done that in the first place. I would recommend that you keep reducing the matrix into the reduced row echelon form which is the identity matrix. Then you have it solved in matrix form. Putting into equation form is only useful when you have a rank deficient matrix and thus have a free variable.

[wass420]

It's not your cup of tea, most people will need coffee. lol

[marcolivi3r]

Thank you



[LAnonHubbard]

Nice one. I'm gaining a lot of intuition about the linear algebra topic which I know I'll be able to use as I'm a computer programmer in the 3D graphics business.

[Frenchy1736]

missed 2 periods of my college math class, and of course we learn the impossible stuff on those days. anyways thanks man you saved me from the torture that is text book terminology. great job, and keep it up!!!

[popachris101]

wow you have just brought my love for algebra to a new level. whatever you are doing keep doing it =]

[iKristina1980]

wow, 5 minutes in and I was tired of hearing his voice. You really need to eliminate unnecessary information. It overshadows what your teaching. I agree without sound I learned alot more. Straight to the point, then babble about whys.

[MrTremelocity]

@iKristina1980 How are you supposed to truly learn without knowing why?

[Lucy0is0on0drugs]

when i tried solving x+y+z=1—①

5x+9y+13z=17—②

4x+y-2z=-5—③

the answer was 0=0. Does this mean that the planes have infinately many solutions? In that case, how do i find the point where they intersect at one point? Please help, I need this for my maths portfolio.

[Bronnil858]

@Lucy0is0on0drugs They lie on the same line they are coincedent so they are same line all points touch.

[histand]

Very helpful for linear algebra clarifications. You are gifted.

[starfish53]

I would suggest to viewers to try to watch it without sound.  You can learn more that way I think

[SpoiledLogic]

@starfish53 Cool suggestion! Thanks!

[refined711]

Hey Sal, cool video :)

Could you please do one explaining Idempotent Matrices and their application? I can't seem to find much easy to understand material about it on the internet

Keep up yhe good work! xx

[ABCba5tard]

y= 0 and u said y = 10 lol

[Jakers2009]

making a simple error shows sal is human - i think the fact which makes him amazing is that he understands all of the processes not to mention how inutuitive sal must have been when in class. Just think sal doesn't differentiate between arethmetic and linear algebra when he teaches - the fact of the matter is that he understand all of these with the minimum effort. "-(-2) wtf" if thats the best you got please dont bother!

[SpoiledLogic]

@Jakers2009 Agreed!

[aeiou2304]

wth

[mohth]

Tthx alot...

you r a great man.

[madscirat]

Poor Mrs. Khan, she must share her hubby with the nerds of the world. LOL

[baseballkid077]

or you can plug these numbers into a calculator using the matrix function and get x,y, and z in no more than 30 seconds.

[mcmuffinburger]

OMG I LEARNED SUBSTITUTION AND ELIMINATION!!!!

and every1 in my class and other algebra classes do not understand this...but now i have found it is relatively simple

[Boontoon]

Very Thanks!!

[cdlsoldier]

nice, ive been having such a bitch of a time lately since i totally zoned out for my last 3 classes. good video, im on top of things now

[wondergirlsy]

I don't get how -y can become y

[Hroros]

One of the best vids on utube. thanks! perfectly explained.

[dubey666manu]

its so easey :|

[Dimitrijesolar]

does this work with more than 3 variables?

[Dimitrijesolar]

Does this work with 4 variables? I rly need to know... :S

[clixsyt]

@Dimitrijesolar

Yup. It will be a 4x5 matrix instead of a 3x4.

[madscirat]

@Dimitrijesolar As long as you have 4 equations yes.

[SlipryFingrz]

thanks i learned a new way to solve this lol maybe this might be easier than the last one...

[jacksjunkie]

wow this video really helps to understand them. thanks

[kylemartin3]

Hahahaha. I love the ending. :D

[MrCoolguy6273]

as soon as you put +4 there i got lost then the correction thing came in haha

[Travellersfees]

This is the same as just solving simultaneous equations algebraically in the way I was taught at secondary school!

The only difference is substituting the letters with a position on the grid (i.e. row 2 means y).

Is there a case where this is significantly more convienient than merely applying this 'algorithm' to the equations themselves?

Thanks.

[yynotx]

loved the phone interuption at the end--classic

[protestchiodos]

kudos Sal rockin the lin alj videos like mad givin me somethin to watch i appreciate it. You the man.

[coolbidman]

great video, i was confused all week, now everything just kinda clicked. so i am getting about 90% of the homework right .

Thanks Khan Academy

Also i was wondering how you made this video.

[EngMido7osam]

cool ,, but very simple

we want some advanced matrices plz

[shugarkiss]

thank you so much this helped a lot!

[LeviJoseph]

sweet

[Remus820]

For anyone who uses an voyage 200 or an ti-89, you can use the function rref (reduced row echelon form) with the augmented matrix and the function will do exactly what he does here, using gauss-jordan elimination :)

[MistaFrista]

I've tried out an exercize from my homework and somehow when I tried to solve for z (by substracting the y value in the 3rd line) I came to a situation where I essentially could substract the y, but it would leave me with an x, or I would lose the y and z simultaneously. I dunno, it may be my error, or some non defined exercize?

x+2y+3z=1

4x+5y+6z=0

7x+8y+9z=0

[ScythePuppet]

No solutions.

[dannyboy12357]

i believe this is called the gauss jordan method

[Barnekkid]

Unless you fool around with Gauss-Jordan/Gaussian elimination all the time an error like -(-2)=4 is easy to make. As you say, this stuff is computationally intense, and it's also deceptively complex.  5 stars, good job.

[rewtguy]

plus it's a pain in the ass to redo a 15 minute video over 1 mistake....

[alearg89]

Dude, i love your videos :D

I wish i had a teacher like you D;

thanks and keep them coming!

[fistylo]

when you are solving this equations.are you thinking about special case in your mind?

[FHomeBrew]

I use this sort of equations when I want a parabola to pass through 3 points (2D). a(x1)²+bx+c = y1 a(x2)²+bx+c = y2 a(x3)²+bx+c = y3 (the numbers by the x and y are indices) If I want a parabola through these points: (-1,1), (2,3) and (4,5), I fill in the x and y values and I get three equations with three unknowns (a, b and c) a*(-1)²+b*(-1)+c=1 a*2²+b*2+c=3 a*4²+b*4+c=5 Which eventually leads to [a=1/15,b=3/5,c=23/15] which means my solution is: y=x²/15+3*x/5+23/15.

[fistylo]

thank you man

[The3GWorld]

Yes I caught [-(-2)] as well. Although as the audience it should be easier to catch and correct mistakes than is the presenter. Luckily, it came down to the same conclusion. Sweet!

[solarisgalrocks]

take the first equation and solve for x , so x = (-20+7y+2z/3) Take that whole expression and plug it wherever there's x and keep on solving lol what a mess

[chopperhead2011]

I was going to make a program on my calculator that does this. After I did a proof on paper, I found out that there were too many variables. The system of equations that I solved was:

AX+BY+CZ+D=EX+FY+GZ+H

IX+JY+KZ+L=MX+NY+OZ+P

QX+RY+SZ+T=UX+VY+WZ+X

I used X as the one of the variables I solved for and as a constant term. OmG!

[pxxner]

so -(-2) = 4? wtf....

[khanacademy]

you're right. my brain was tired. I've added annotations to correct.

[zainahmed1994]

@khanacademy no pronlem.. you were hurrying for dinner.. :)

[Ralajer]

Mathematicians "always" mess the arithmetic.

[Ralajer]

Like I mess "up" my sentences and I have no excuse I am not literary scholar.

[DesiGuyTV]

@pxxner It gets pretty hard because it's so computationally intense. lay off, he added the annotations gosh!

[AmishAcorns]

nice informative video