What I love about Khan Academy is that, even though Sal gets millions of views on his channel, its not monetised, which could generate tons of income. I HATE waiting for ads to load if I'm trying to watch a UA-cam video, esp if I'm revising and trying to get through a ton of material in one day. Thank you so much Sal, you've helped me and millions of others. You should be proud of yourself fella.
I rmb how I gave up on academics in my early years when learning matrix. Now revisiting for nostalgic reason, if I can go back I would have given up again
I just wanna say thank you so much. I've never done linear algebra in my life before and I'm writing an exam in two weeks... I was stressing so much but with your videos, i'm understanding it all and actually doing it. You explain it so well, you make it so easy to understand. Thank you!!
@Elemental King I went to the lowest performing school in NH and they lost their acreditation the year after I graduated so I didn't exactly get top tier middle and high school education. But now I have work with Karl Slifer at UNH with one of his experiments down at the Jefferson Lab particle accelerator so HS quality really doesn't matter anymore.
He starts the video: "We will now start the video with what is my least favorite exercise in mathematics." me: turns off he laptop and goes to sleep. Haha, If the teacher doesn't like it, what am I doing.
Math test tomorrow, Khan is like a life jacket, its the only thing keeping me afloat. Now, to cram and crunch info for the next hour and a half. *CRAM CRAM CRAM CRAM CRAM*
Feels weird that I was just learning how to use letters in place of numbers when this video was published and now I'm here studying for college level calculus. But also your videos have been just as essential to me as the videos provided with my ebook.
You have no idea of how much of a lifesaver you are! For the past 3 weeks I've just been going "WTF is this?!" in my math class... This is much simpler then the way my teacher taught me, her way is so confusing, It hurts my brain to try and remember! Thank you!!
Det(A) = 1 - 0 + -2 He messed up the plusses and minuses with determinate but because the second part of the determinate was 0 anyway it didn't affect it. So those who are getting 3, are doing 1 + 0 - -2, but yeah the plusses and minuses go + - +, not + + -
You are such a amazing teacher.. hope one day I will meet you in person.... during lectures in class I though I will never understand but u made it so easy to comprehend.... thanks you so much sir..... maths genius
Good job ! U got it right of course, I multyplied it out and as expected it gives me the Identity matrix .nOW i UNDERSTAND WHY U DISLIKE THEM..I JUST HOPE ITS NOT GOING TO BE ON MY MIDTERM !THANX A LOT, UR GREAT !
nicely explained sal, it's been a long time for me doing matrices there was a slightly mistake as the result should be -1 1 2 in the first row when you were multiplying by co factors matrix could you provide me with a linear algebra text book "name" that is good since I studied all this in french I would like to look it over again in English I appreciate it, thanks for all your efforts to spread knowledge in all different fields for free to all people
My professor told me to do this by row operations to turn the original matrix into an Identity Matrix, repeating the same steps in an equally large Identity Matrix that would then turn into the inverse matrix. Way way harder than using determinants
universally speaking if you have 4x4 matrix r11 r12 r13 r14 r21 r22 r23 r24 r31 r32 r33 r34 r41 r42 r43 r44 to get equivalent + or - you just use indexes of matrix elements like this: (-1)^(i+j) for every element. for example, if you use r32: (-1)^(3+2) = (-1)^5 = -1 so you put "-" to corresponding place
This stuff is hard, but imo this is much easier and faster than the Gauss-Jordan version we were taught, especially since this is the way we were shown for 2x2
If you have a graphing claculator there is a really easy way to do this........ Skip all steps...... Put your matrix in as a 3x3 and fill the number in. Then get this on your calculator screan [A] and use the x^1 button on the left of the calculator so it says................. [A]^-1.............. push enter. Answer... Easy as pie :)
There is a different way of doing it by using Gaussian Elimination with the nxn matrix and the identity matrix and trying to manipulate it so that it ends up the identity matrix and then the (nxn)^-1 matrix
Im literally here for a college junior level business class because I never learned matrices in high school. Went all the way to applied calc and never had a problem until now oof
We had to invert a 5x5 matrix of an economic model, and do all the related operation with a 5x5 matrix for an assignment. We were given 6 days to complete. Seemed a bit unfair
Thank you! Its absurd how much better you are than my lecturers, I would be screwed without your channel.
What I love about Khan Academy is that, even though Sal gets millions of views on his channel, its not monetised, which could generate tons of income. I HATE waiting for ads to load if I'm trying to watch a UA-cam video, esp if I'm revising and trying to get through a ton of material in one day. Thank you so much Sal, you've helped me and millions of others. You should be proud of yourself fella.
you can use adblocker to avoid the ads
@@Bouryal.Y I am not sure if those really worked on UA-cam 9 years ago. But yes, I myself too, use an adblocker.
I rmb how I gave up on academics in my early years when learning matrix. Now revisiting for nostalgic reason, if I can go back I would have given up again
I just wanna say thank you so much. I've never done linear algebra in my life before and I'm writing an exam in two weeks... I was stressing so much but with your videos, i'm understanding it all and actually doing it. You explain it so well, you make it so easy to understand. Thank you!!
Bruh algebra 2? I’m a second year physics major in university and we are just learning this now.
I am 12 years old.
I am a freshman learning this
@Elemental King
I went to the lowest performing school in NH and they lost their acreditation the year after I graduated so I didn't exactly get top tier middle and high school education. But now I have work with Karl Slifer at UNH with one of his experiments down at the Jefferson Lab particle accelerator so HS quality really doesn't matter anymore.
I'm a freshman learning this the second week :(
@Elemental King depends where you are. In some CA schools they don't even teach matrices in Pre calculus.
"if i keep doing this my whole life it'll stop my brain from degrading"
one of the many salman khan win moments
Omg... why did I find you only today?
Thank you so much, you just become my Math guider, better than my professor.
He starts the video: "We will now start the video with what is my least favorite exercise in mathematics."
me: turns off he laptop and goes to sleep.
Haha, If the teacher doesn't like it, what am I doing.
I have a final tomorrow and I basically learned the whole semester in 10 hours straight on youtube lol
I AM SO GLAD I AM NOT THE ONLY ONE
@@nhutran2000 its possible, but I didn't get the best grade overall lol..
LMFAO prevent my brain from degrading
Math test tomorrow, Khan is like a life jacket, its the only thing keeping me afloat. Now, to cram and crunch info for the next hour and a half. *CRAM CRAM CRAM CRAM CRAM*
one of the best channel ever. thank you sir
Wow... I think I'll just stick to inverting 2X2 matrices for now 😂
Wish i could say that to my teacher lmao
exactly this was me 3 years ago.....now I am forced to do that......lolz .....well actually I chose it myself (hahahah)
Feels weird that I was just learning how to use letters in place of numbers when this video was published and now I'm here studying for college level calculus. But also your videos have been just as essential to me as the videos provided with my ebook.
55-minute lecture, and I leave the room scratching my head.
17-minute khanacademy video, full understanding.
Thank you.
You have no idea of how much of a lifesaver you are!
For the past 3 weeks I've just been going "WTF is this?!" in my math class... This is much simpler then the way my teacher taught me, her way is so confusing, It hurts my brain to try and remember!
Thank you!!
Inverting a 4×4 matrice is like living harry potters life
This is the best use of youtube!... thanks youtube and obviously Khanacademy!...
Det(A) = 1 - 0 + -2
He messed up the plusses and minuses with determinate but because the second part of the determinate was 0 anyway it didn't affect it.
So those who are getting 3, are doing 1 + 0 - -2, but yeah the plusses and minuses go + - +, not + + -
VT Gaming Yeah it would be 3
No he did not mess the signs because he has already multiplied the minor determinants by + - + in the cofactor matrix
Our teacher barely teaches this and im a sophomore in highschool, thank you for this explanation!!
You are such a amazing teacher.. hope one day I will meet you in person.... during lectures in class I though I will never understand but u made it so easy to comprehend.... thanks you so much sir..... maths genius
my man really out here saving lives
Good job ! U got it right of course, I multyplied it out and as expected it gives me the Identity matrix .nOW i UNDERSTAND WHY U DISLIKE THEM..I JUST HOPE ITS NOT GOING TO BE ON MY MIDTERM !THANX A LOT, UR GREAT !
Thou hath conquered the mighty 3x3 matrix inversion. Huzzah!
my teacher gave us 4*4 and 5*5 to do -.- RIP me
what is wrong with your teacher.
fr man! idek
LOL
Lol!
Well it will help ur brain from degrading
Use the matrix inverse algorithm for matrix larger than 2*2, which is much much simpler to find inverses .
We need lecturers like you !
I really don't know why I bother with my professors when even twelve year old videos from Salman help me understand concepts in less than 20 minutes.
nicely explained sal, it's been a long time for me doing matrices
there was a slightly mistake as the result should be
-1 1 2 in the first row when you were multiplying by co factors matrix
could you provide me with a linear algebra text book "name" that is good
since I studied all this in french I would like to look it over again in English
I appreciate it, thanks for all your efforts to spread knowledge in all different fields for free to all people
all this crazy ass shit for a 3x3 matrix
I used this video to answer a quiz question and I arrived at the correct answer! thank you for posting this informative video.
OMG you're a legend Sal, I just did a 3X3 plopped it into a calc, and that sweet feeling when every entry was right.
Really great, well explained, simple !!
I've never learnt that before and following the steps with you gets my head around matrices !!!
Cheers!
ur the saint in math!!!!!!!!!!!!!!!
Dude you just saved me my exam...
Keep up the awesome work!
thx from sweden
"It will prevent my brain from degrating" That was funny :D Thanks again for your hard work, you're the modern kind of a superhero.
wow i can't believe this comment was made 11 years ago. I feel like i'm in a time warp
god bless this man. Honestly.
Khan, you are the Plato of the 21st century. Thank you, I really thank you
Oh... my... GOSH!!! I UNDERSTAND MATH!!!
these concepts were in my 12th std pu syllabus due to some reason i had forgotten them all thanks to u it's all coming back
Thank you Khan. I am from Hong Kong
My professor told me to do this by row operations to turn the original matrix into an Identity Matrix, repeating the same steps in an equally large Identity Matrix that would then turn into the inverse matrix.
Way way harder than using determinants
you are a true hero!
universally speaking if you have 4x4 matrix
r11 r12 r13 r14
r21 r22 r23 r24
r31 r32 r33 r34
r41 r42 r43 r44
to get equivalent + or - you just use indexes of matrix elements like this:
(-1)^(i+j) for every element.
for example, if you use r32:
(-1)^(3+2) = (-1)^5 = -1 so you put "-" to corresponding place
Thanks again Sal you are the best it cn get confusing ikr 😅 buh will mke tt smehw
thanks man....ur a legend.....trying to figure this out for a long time.
Excellent explanation.Thank u.
ur method of teachibg is best...
This stuff is hard, but imo this is much easier and faster than the Gauss-Jordan version we were taught, especially since this is the way we were shown for 2x2
Try this with fractional values and you be the BOSS man!
Thank you very much khan academy!😘
Give that man a Nobel prize, Khan.
Thank you this helped me a lot. A lot of other people were using stupid methods but this one is so easy to understand
You just did me a huge favor. Thanks Khan!!
Thank you so much! I have such a hard time studying
is 'inverting' a matrix the same as finding the 'inverse' of a matrix?
No
what?
Which Mathematician had come up with this idea?
If you have a graphing claculator there is a really easy way to do this........ Skip all steps...... Put your matrix in as a 3x3 and fill the number in. Then get this on your calculator screan [A] and use the x^1 button on the left of the calculator so it says................. [A]^-1.............. push enter. Answer... Easy as pie :)
just realised this vid is 14 years old, WOW
so good I have learnt sth from ur vids
I think the determinant of 3*3 matrix is -3. I calculated it in both ways you explained in video and the answer came out to be -3.
Really good explanation.
thanks a lot for this technique. I think this is less confusing than the elementary row operation.
omg thank you so much, this made learning how to swap frames from a 3x3 inverse matrix into a different frame
I don't know why, but this method seems to be easier than the Gauss-Jordan method for me. Thank you for this video!
There is a different way of doing it by using Gaussian Elimination with the nxn matrix and the identity matrix and trying to manipulate it so that it ends up the identity matrix and then the (nxn)^-1 matrix
This is DEFINITELY better than how my COLLEGE TA tells us to do it... Thank you SO much.
If every lesson in each course I had is this clear, I'd definately become an engineer
gods truth thank god for this video this is such a long stupidly complex process
Thanks you saved my life
Thx, clear & simple!
great videos, all of them. above university standard..
Khan for president :D
I'm amazed you didn't make a mistake =D. Got the identity matrix when multiplied those two together ^^
Fantastic sal...
thanks..that helped
Great video. I watch all of them. Thank you for taking the time out of your day to create these.
YOU ARE AWESOME!!!!!!!!!
I think just combining it with the 3x3 identity matrix & using gauss jordan is easier to get the inverse. Just like a 2x2, only bigger.
gabrieltnc1 Gets you the same answer in less time.
oh wow, that makes it much easier! thanks man!
Dude....Props...
watching this in 2020 be like wth
Right😂
Is the checkered board always applicable to start at a positive sign or to start it off with the sign opposite to the 1st number in the first row?
Its easy because he always chooses easy numbers. Its easy to solve inverse matrix with 0 and 1.
What kind of fucking evil shit is this. Still a great video but this matrices shit is like ahhhhgggh
this is called wizardry and sorcery, a few years ago was forbidden and those committing were burned AAALIVe
This is crazy!
lol the part he said only take 17 minutes .... Helpful though
EPIC u should make a video for cramming for the SAT's
This 3 by 3 matrix is eating my brain away 🤯 But I’m learning so that’s good!!
thank you !
Thank you so much master! many blessings and thanks!
Hello Mr Khan
Thank you very much for this awesome lecture.
Im literally here for a college junior level business class because I never learned matrices in high school. Went all the way to applied calc and never had a problem until now oof
So nice thanks
I came to learn how to solve linear systems of equations. I was innocent enough to think it would make my life easier.
Hey Sal, thanks for the great video! :) But how do you apply this for a 4 by 4 or n by n matrix?
This helped so much! Thanks so much Khanacademy :3
We had to invert a 5x5 matrix of an economic model, and do all the related operation with a 5x5 matrix for an assignment. We were given 6 days to complete. Seemed a bit unfair
more like matrix of minor annoyance... great video thank you from Canada
Good friends with the polynomial of partial inconvenience
I can't believe they teach this stuff in highschool. Uni math is more like.. graph theory, base 5 numbers.. etc.