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 TH-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.
@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 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!!
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 + + -
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.
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
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 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 !
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*
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!!
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
There is a MUCH simpler way to do this by setting the matrix A equal to the identity matrix then row reducing until you get the identity matrix on the left. Then what you are left with on the right (where you started with I) is your inverse A
Kyle K That is the worst way you are telling I mean that's much more complex than this one There are easier methods to solve a matrix than in the video but what you are talking is the worst Elementary Reduction > The method in the video > The method I use ^Order of easiness
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 :)
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
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
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
just a question, can you only get the inverse of a matrix if it's a square matrix? or can you do it with any matrix with any number of columns and rows?
If you augment the Identity matrix of whatever of A is and then get the RREF of A while also performing the same row operations on the identity matrix. The identity matrix will be there inverse of A after you get A to be RREF.
You can make these kinds of calculations much easier for yourself if you use variables in the original 3*3 matrix (say, from a to i, in other words, the 9 different numbers represented by 9 letters), and then calculate everything until you reach the inverse matrix. That way you can simply look at any 3*3 matrix and input the numbers in the inverse matrix and you are done.
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 TH-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 TH-cam 9 years ago. But yes, I myself too, use an adblocker.
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.
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!!
"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.
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
Inverting a 4×4 matrice is like living harry potters life
one of the best channel ever. thank you sir
Use the matrix inverse algorithm for matrix larger than 2*2, which is much much simpler to find inverses .
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
is 'inverting' a matrix the same as finding the 'inverse' of a matrix?
No
what?
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.
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
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.
Really great, well explained, simple !!
I've never learnt that before and following the steps with you gets my head around matrices !!!
Cheers!
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
all this crazy ass shit for a 3x3 matrix
my man really out here saving lives
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
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.
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
55-minute lecture, and I leave the room scratching my head.
17-minute khanacademy video, full understanding.
Thank you.
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)
Facts.
We need lecturers like you !
Our teacher barely teaches this and im a sophomore in highschool, thank you for this explanation!!
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.
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?
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 !
This is the best use of youtube!... thanks youtube and obviously Khanacademy!...
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*
I used this video to answer a quiz question and I arrived at the correct answer! thank you for posting this informative video.
Hey Sal, thanks for the great video! :) But how do you apply this for a 4 by 4 or n by n matrix?
Great video. I watch all of them. Thank you for taking the time out of your day to create these.
omg thank you so much, this made learning how to swap frames from a 3x3 inverse matrix into a different frame
why do you only take the values from the first row? for determinate of [A]?
maestropasser you should read your books also
@@eye1158 you should answer the question and give help instead of being a jerk
im wondering the same thing
god bless this man. Honestly.
Thanks again Sal you are the best it cn get confusing ikr 😅 buh will mke tt smehw
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!!
Thank you so much! I have such a hard time studying
Thank you this helped me a lot. A lot of other people were using stupid methods but this one is so easy to understand
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.
Khan, you are the Plato of the 21st century. Thank you, I really thank you
Thou hath conquered the mighty 3x3 matrix inversion. Huzzah!
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
you are a true hero!
Dude you just saved me my exam...
Keep up the awesome work!
thx from sweden
Thank you Khan. I am from Hong Kong
ur the saint in math!!!!!!!!!!!!!!!
I'm amazed you didn't make a mistake =D. Got the identity matrix when multiplied those two together ^^
Excellent explanation.Thank u.
ur method of teachibg is best...
Try this with fractional values and you be the BOSS man!
thanks a lot for this technique. I think this is less confusing than the elementary row operation.
thanks man....ur a legend.....trying to figure this out for a long time.
Thank you very much khan academy!😘
You just did me a huge favor. Thanks Khan!!
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
I don't know why, but this method seems to be easier than the Gauss-Jordan method for me. Thank you for this video!
so good I have learnt sth from ur vids
There is a MUCH simpler way to do this by setting the matrix A equal to the identity matrix then row reducing until you get the identity matrix on the left. Then what you are left with on the right (where you started with I) is your inverse A
I believe Khan introduces that method in one of the matrix videos.
Kyle K That is the worst way you are telling
I mean that's much more complex than this one
There are easier methods to solve a matrix than in the video but what you are talking is the worst
Elementary Reduction > The method in the video > The method I use
^Order of easiness
@@firefeathers4058 using row and column transformation is worse than getting stuck in a bear cage.
Really good explanation.
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 :)
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
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
Oh... my... GOSH!!! I UNDERSTAND MATH!!!
gods truth thank god for this video this is such a long stupidly complex process
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
Part 2 is an alternate way using RREF and junk. Much easier. My course didn't even touch on the methods mentioned in this video.
This is DEFINITELY better than how my COLLEGE TA tells us to do it... Thank you SO much.
How do you know the steps for this? Very interested to learn the proof and history behind this.
"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
YOU ARE AWESOME!!!!!!!!!
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.
just a question, can you only get the inverse of a matrix if it's a square matrix? or can you do it with any matrix with any number of columns and rows?
oh wow, that makes it much easier! thanks man!
thanks..that helped
If you augment the Identity matrix of whatever of A is and then get the RREF of A while also performing the same row operations on the identity matrix. The identity matrix will be there inverse of A after you get A to be RREF.
This helped so much! Thanks so much Khanacademy :3
thank you !
Thx, clear & simple!
EPIC u should make a video for cramming for the SAT's
What is the difference between transpose of a matrix and adjoint of the matrix??
You can make these kinds of calculations much easier for yourself if you use variables in the original 3*3 matrix (say, from a to i, in other words, the 9 different numbers represented by 9 letters), and then calculate everything until you reach the inverse matrix.
That way you can simply look at any 3*3 matrix and input the numbers in the inverse matrix and you are done.
This is crazy!
So nice thanks
Thanks you saved my life
Fantastic sal...
Dude....Props...
great videos, all of them. above university standard..
Thank you so much master! many blessings and thanks!
Give that man a Nobel prize, Khan.
Hello Mr Khan
Thank you very much for this awesome lecture.
For matrix of minors, the element for row 1 column 3 is incorrect, right? it should be -1 instead of -2.
thanks man
If every lesson in each course I had is this clear, I'd definately become an engineer
Shouldn't the det(a) =-3 ???
very nice, thx