Heads up, people: be sure to watch with notations turned on so you can see the corrections. I actually really like this video not only because it's definitely helpful but also because seeing one of my personal heroes make a mistake on what are very simple operations (which, as we can see, become challenging as they are compounded together into one big computationally-intensive problem) is very reassuring to me in a way, because I've made similar mistakes in the past while working on stuff like this and then felt stupid or shameful when I realized I made those mistakes. Another thing related to that is that in working on problems like this, it becomes less of a wonder that we often hear Sal repeating himself as he is narrating the process of solving the problem(s) in the videos. It can help keep the mind focused when you hear yourself say what you're doing like that. Bright people who are mentally quick may also be very prone to daydreaming, and random thought distractions happen to everyone, so it's no wonder we find ourselves making mistakes on simple things sometimes. But yeah, cool video. :)
Giuseppe Jones 1: Don't start sentences with "but", it is bad grammar. 2: *you're not a genius, you're probably as smart as a turd and uglier than one too. 3: You managed to make 5 grammatical errors in one sentence. 4: I do not know why I am even commenting back to you.
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 :)
Thank you so much. My teacher gave me homework over vacation using our textbooks to teach three weeks of work to ourselves! Needless to say I don't understand it just by reading it, so thank you for explaining!
@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.
Thank you so much!! I've been trying to figure these out for days. My teacher taught the same things, but for some reason how you said it just made all the fog clear.
For anyone that is confused this is done to eliminate the x coefficient in both Equation 2 and 3, and the Y coefficient from Equation 3 doing so makes solving for z as simple as dividing the multiple of z by what is on the other side of Equation 3 then you put what z is equal to into equation 2, allowing you to solve for Y, finally you are able to put both Y and z into Equation 1, which gives you the solution
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.
thank you khan, now it's a lot easier to understand guassian ellimination. We were told about guassian ellimination in class, but it was like looking to deep deep scary forest for an hour :D thank's a lot!
I'm giving a problem like this to my 4th grade Math Olympiad class. It doesn't include variables, but instead geometric figures. I followed the instructions exactly as he explains, and it worked like a charm. The problem is that there's no way that this problem was meant to be solved this way by 4th graders. I don't ever look up answers to problems for this class, so once I see the explanation given, I'm sure I'm going to see a very clever solution that doesn't include Gaussian elimination.
+TheSamuraiApocalypse He used an annotation to say it should be 2, not 4. I usually keep my annotations off because other users use them for ads and other annoying junk. I haven't seen Khan Academy do this.
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.
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.
In these older videos, Sal sounds as if he has just got out of bed and is in a pleasantly groggy state, and is like "aaah, yeah, that video - let's do it...".
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.
in the last video, you said there can be 2 points of contact if there are 3 equations. Here, there are 3 equations but how is it possible to get 2 points of contact. Like how would the answer look like? example (1,2,3) and (1, -2, 3)? just a negative on one of the x or y or z?
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.
would i get the same answer if i got rid of the 2y from the 3rd equation by multipying the first equation by -1 and then adding that result to equation 3?
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!
***** Yes you would basically use the same procedure, it would just be very computational. Your best bet would just to use matrices in the form Ax=b where A is your coefficients, x is a vector of your variables [(w,x,y,z) for 4 variables] and b is a vector of your intercepts. Then just do x = A^-1*b to solve. He does this in earlier videos for a two by two matrix.
- (-2) is equal to +2, NOT 4.
Solving for this, you get x = -1
Put that into the original equation: - (-1) + 2(3) - (-2) = 9
Who cares, it's about the method :/
Omg I thought No one else saw it and yes you are correct :)
Put on your notifications, he corrects himselve.
Every body makes mistakes
It's obvious it's just a simple mistake
Heads up, people: be sure to watch with notations turned on so you can see the corrections. I actually really like this video not only because it's definitely helpful but also because seeing one of my personal heroes make a mistake on what are very simple operations (which, as we can see, become challenging as they are compounded together into one big computationally-intensive problem) is very reassuring to me in a way, because I've made similar mistakes in the past while working on stuff like this and then felt stupid or shameful when I realized I made those mistakes.
Another thing related to that is that in working on problems like this, it becomes less of a wonder that we often hear Sal repeating himself as he is narrating the process of solving the problem(s) in the videos. It can help keep the mind focused when you hear yourself say what you're doing like that. Bright people who are mentally quick may also be very prone to daydreaming, and random thought distractions happen to everyone, so it's no wonder we find ourselves making mistakes on simple things sometimes. But yeah, cool video. :)
you're right. my brain was tired. I've added annotations to correct.
Get distracted by Instagram, no i would never!
get distracted by a guy going to eat out (WITH) his wife in his math video?
absolutely.
Hope u people are doing well however it's been 15 years!
I have no idea what just happened.
tbh
It is easy :D
Me neither
"I'm suppose to go eat out...(my wife)" ran through my mind lol.
14:49 for the impatient among us
@@ozzyfromspace among us
Yep me too :D
@@ozzyfromspace thanks 😁
If my teacher was like you I'd be a genius by now
Lobster with Mustard and Rice
but your not genius, your probably as smart as a turd and uglier then one to.
Giuseppe Jones
1: Don't start sentences with "but", it is bad grammar.
2: *you're not a genius, you're probably as smart as a turd and uglier than one too.
3: You managed to make 5 grammatical errors in one sentence.
4: I do not know why I am even commenting back to you.
Giuseppe Jones GET REKTT HAHAAHAA
Lobster with Mustard and Rice I don't go to classes I only watch his videos
Shakil Rahman Giuseppe Jones is just a troll. It is best to not give him any attention.
Man I wish you taught me math instead of my professor
I love to watch your videos when I'm high. You are very smart, sir.
Thank you! Got more than this than a whole lecture!
+Nick Jones-same bro
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 :)
You solve them way more complicated than I learned in the past.
Thanks a lot Sal, you're style of teaching is so clear and simple, this has really helped me
Thank you so much. My teacher gave me homework over vacation using our textbooks to teach three weeks of work to ourselves! Needless to say I don't understand it just by reading it, so thank you for explaining!
I love how emphasized the connection with solving simultaneous equations. That made the whole thing click for me.
12:40 "Just for kicks". Oh, stop it, you! Still the man all along, Sal!
Late but I love just for kicks :)
@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.
God help us
Afrahhussain this shits easy just pay attention
Love this comment. 😌
Thank you so much!! I've been trying to figure these out for days. My teacher taught the same things, but for some reason how you said it just made all the fog clear.
if i saw this two years ago, i'd have passed my exam so easily. good job man!
For anyone that is confused
this is done to eliminate the x coefficient in both Equation 2 and 3, and the Y coefficient from Equation 3
doing so makes solving for z as simple as dividing the multiple of z by what is on the other side of Equation 3
then you put what z is equal to into equation 2, allowing you to solve for Y,
finally you are able to put both Y and z into Equation 1, which gives you the solution
Just used this to help me solve an electrical engineering problem for uni. Hurrah for Khan!
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.
thank you khan, now it's a lot easier to understand guassian ellimination. We were told about guassian ellimination in class, but it was like looking to deep deep scary forest for an hour :D
thank's a lot!
You are simply amazing! I value your work to the extreme Sal!
I'm giving a problem like this to my 4th grade Math Olympiad class. It doesn't include variables, but instead geometric figures. I followed the instructions exactly as he explains, and it worked like a charm. The problem is that there's no way that this problem was meant to be solved this way by 4th graders. I don't ever look up answers to problems for this class, so once I see the explanation given, I'm sure I'm going to see a very clever solution that doesn't include Gaussian elimination.
Very helpful for linear algebra clarifications. You are gifted.
wish i had this guys brains for my exam tomorrow!!
"I'm just writing it in a form that has a little bit less...letters in it." lol, this guy is great.
One of the best vids on utube. thanks! perfectly explained.
wow you have just brought my love for algebra to a new level. whatever you are doing keep doing it =]
It starts at 3:30
I'm living in this man's beard.
How did he get 4 out of -(-2)? Shouldn't that've just been 2? It's at the end.
+TheSamuraiApocalypse He used an annotation to say it should be 2, not 4. I usually keep my annotations off because other users use them for ads and other annoying junk. I haven't seen Khan Academy do this.
Precisely......
Yes, it should be two instead of four
Dude, i love your videos :D
I wish i had a teacher like you D;
thanks and keep them coming!
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.
Thankyou sooo much , you have really made a difference to my studies.
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.
Sal khan is the man!
15:23 he is getting laid.
So honey, at what point do you think our surfaces will meet?
14:57 more specifically, he is planning to, ''eat her out''.
Harki Singh dude he said his wife is downstairs and he is going to eat out. HE IS GOING TO EAT HER OUT
which intuition video that Sal just mentioned ?
Thanks for the explanation Sal.
I absolutely love your videos! They are really making a massive difference with regards to my marks for university.
14:53 the solution is omg my phone is ringing. I KNOW ALL THE MATHZ
When it comes to eliminating "6".. Can I use the first equation? Or you always have to use the second equation?
Thanks for another great video!
In these older videos, Sal sounds as if he has just got out of bed and is in a pleasantly groggy state, and is like "aaah, yeah, that video - let's do it...".
Still the best😭 thnx from students of Shyngys agai💘
shouldnt x be -1
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.
I would suggest to viewers to try to watch it without sound. You can learn more that way I think
I love your idiosyncrasy
+Khan Academy why is the next video not working? the one were you introduce us to vectors. it says its private. hope it gets fixed soon :)
@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.
2:14 minor explaining mess up (y is equal to zero, as he writes) 10:40 minor mess up with -but thanks so
My favorite part........when his wife called.......from downstairs
😂😂🔥🔥
You are awesome!!!!! Please come and teach in Hawaii!!!! PLEASSSSSSSSSE!!!!!!!
Tq sir lucid explanation....liked & subscribed
Got it. Thanks Khan. 👍
Fantastc video, thanks heaps, you’re amazing.
in the last video, you said there can be 2 points of contact if there are 3 equations. Here, there are 3 equations but how is it possible to get 2 points of contact. Like how would the answer look like? example (1,2,3) and (1, -2, 3)? just a negative on one of the x or y or z?
Nice on bro, u re a genius. A quick observation though -(-2)= +2 not +4 when solving for x. But thanks for your efforts.
Thanks for taking the time out to help even though your wife was ready for dinner. I'm a wife myself so I know she was starving!! lol
Lol :3
what about the elementary row operations? I never saw you interchange rows or explain those laws.
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.
Thank you sir! Easy to follow!
2019?
Nah 2021 lol😆
Awesome
So easy way
Thanks
when you are solving this equations.are you thinking about special case in your mind?
he multiplies the first equation with 3, so if you multiply -y (also -1 y) with 3
you get 3 . (-1 y) which gives you -3 y
What do you do when 2 of the points are the same because one is a toppoint and the other is just a given point?
How do I find out how to solve two equations with two unknowns?
I know I'm like 6 years late but if for some reason you still haven't figured it out, check out simultaneous equations before u get into matrices
how about equations with 4 unknowns like in the Lagrange multiplication?
would i get the same answer if i got rid of the 2y from the 3rd equation by multipying the first equation by -1 and then adding that result to equation 3?
Careful sir x= -1 ;) And thanks for this amazing content
nice informative video
wow this video really helps to understand them. thanks
Great job, but the solution set is (-1,3,-2).
why cant you be my teacher for all my subjects :(
Could you explain this topic in another way, Please... Thank you
Thank You a lot, You helped me understood this thing..
Did he mention the triangular form before he mention the matrix?
Tthx alot...
you r a great man.
wow you really like your colors
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!
how did you get the 4 in (-x+6+4 = 9)? isnt the 4 suppose to be a 2....
-x+6+4=9 how did -z which was -2
Became 4???
I didnt understand ....
Did u multiply it by 2? Again??
It wasn't supposed to. That's an error. In the end the answer should be the point (-1,3,-2) not (1,3,-2).
you do it exactly like this one with 3, you put de numbers in a matrix and solve it like he did (he used the method of Gauss-Jordan)
You should make a video on solving two unknowns and two equations
boi...
Ntnsity what
@ 01:27 were did u get the 3 from??
4:52 teacher might be upset or impressed.
You are the real MVP ;)
is it possible to solve equations with 3, 4, 5 or even more unknowns with matrices??
***** Yes you would basically use the same procedure, it would just be very computational. Your best bet would just to use matrices in the form Ax=b where A is your coefficients, x is a vector of your variables [(w,x,y,z) for 4 variables] and b is a vector of your intercepts. Then just do x = A^-1*b to solve. He does this in earlier videos for a two by two matrix.
Hats off to you !!
why -(-2)= 4
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 ^^.
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
Thank you my savior
Please explain how you got 4 when -(-2) : 2
You are awesome but maybe it's nice if you correct the mistake to avoid confusion. As some people said, x = minus one
Can someone please explain why the -2 at the end turned into 4 I would really appreciate it!