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
@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 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!!
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 RUclips 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.
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 !
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.
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*
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 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
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
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?
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
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
Can someone tell me what do you do when you have 4X4 or 5X5 Matrices? I don't mean the entire process, just the principles. Can you expand what you do in a 3X3 matrix to a 4X4 etc?
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!!
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.
I don't get this... How does this method help us when we are trying to calculate the matrix of minors for a matrix larger than 3x3 (say a 4x4 or 5x5 matrix)? It doesn't look like we would just be left with a 2x2 matrix when we cross out the row and the column for an element in the original matrix... I guess what I'm trying to say is, how do we find the determinant for a matrix with dimensions larger than 2x2? Also, is it only possible to calculate inverses for nxn matrices? What if the number of rows of a matrix does not equal its number of columns? Are we able to calculate the inverse for such a matrix?
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
![GEEK TIMË [OFFICIAL AUDIO]](http://i.ytimg.com/vi/ry-6RvkH880/mqdefault.jpg)
Thank you! Its absurd how much better you are than my lecturers, I would be screwed without your channel.
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
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 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!!
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 RUclips 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 RUclips 9 years ago. But yes, I myself too, use an adblocker.
LMFAO prevent my brain from degrading
Omg... why did I find you only today?
Thank you so much, you just become my Math guider, better than my professor.
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
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.
"if i keep doing this my whole life it'll stop my brain from degrading"
one of the many salman khan win moments
Use the matrix inverse algorithm for matrix larger than 2*2, which is much much simpler to find inverses .
is 'inverting' a matrix the same as finding the 'inverse' of a matrix?
No
what?
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
one of the best channel ever. thank you sir
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?
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.
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..
Thanks again Sal you are the best it cn get confusing ikr 😅 buh will mke tt smehw
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
Really great, well explained, simple !!
I've never learnt that before and following the steps with you gets my head around matrices !!!
Cheers!
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.
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
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 !
all this crazy ass shit for a 3x3 matrix
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.
This is the best use of youtube!... thanks youtube and obviously Khanacademy!...
Inverting a 4×4 matrice is like living harry potters life
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.
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
Excellent explanation.Thank u.
Our teacher barely teaches this and im a sophomore in highschool, thank you for this explanation!!
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.
god bless this man. Honestly.
Thank you this helped me a lot. A lot of other people were using stupid methods but this one is so easy to understand
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.
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*
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.
ur method of teachibg is best...
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
55-minute lecture, and I leave the room scratching my head.
17-minute khanacademy video, full understanding.
Thank you.
thanks a lot for this technique. I think this is less confusing than the elementary row operation.
my man really out here saving lives
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.
What is the difference between transpose of a matrix and adjoint of the matrix??
We need lecturers like you !
How do you know the steps for this? Very interested to learn the proof and history behind this.
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
Thank you very much khan academy!😘
omg thank you so much, this made learning how to swap frames from a 3x3 inverse matrix into a different frame
Khan, you are the Plato of the 21st century. Thank you, I really thank you
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
Dude you just saved me my exam...
Keep up the awesome work!
thx from sweden
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!
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?
You just did me a huge favor. Thanks Khan!!
thanks man....ur a legend.....trying to figure this out for a long time.
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.
Try this with fractional values and you be the BOSS man!
Thank you Khan. I am from Hong Kong
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
Really good explanation.
Thank you so much! I have such a hard time studying
I multiplied A by its inverse to checked if its correct and it is
Can someone tell me what do you do when you have 4X4 or 5X5 Matrices? I don't mean the entire process, just the principles. Can you expand what you do in a 3X3 matrix to a 4X4 etc?
Thou hath conquered the mighty 3x3 matrix inversion. Huzzah!
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!!
Thx, clear & simple!
I used this video to answer a quiz question and I arrived at the correct answer! thank you for posting this informative video.
thanks..that helped
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.
so good I have learnt sth from ur vids
gods truth thank god for this video this is such a long stupidly complex process
This helped so much! Thanks so much Khanacademy :3
EPIC u should make a video for cramming for the SAT's
Sir, why they did not use the same minor and cofactor rule for 2×2 matrix.
What is the real world application (including rocket science) to matrices?
thank you !
I don't know why, but this method seems to be easier than the Gauss-Jordan method for me. Thank you for this video!
ur the saint in math!!!!!!!!!!!!!!!
Thank you so much master! many blessings and thanks!
Hello Mr Khan
Thank you very much for this awesome lecture.
oh wow, that makes it much easier! thanks man!
I don't get this... How does this method help us when we are trying to calculate the matrix of minors for a matrix larger than 3x3 (say a 4x4 or 5x5 matrix)? It doesn't look like we would just be left with a 2x2 matrix when we cross out the row and the column for an element in the original matrix... I guess what I'm trying to say is, how do we find the determinant for a matrix with dimensions larger than 2x2?
Also, is it only possible to calculate inverses for nxn matrices? What if the number of rows of a matrix does not equal its number of columns? Are we able to calculate the inverse for such a matrix?
great videos, all of them. above university standard..
So nice thanks
Thanks you saved my life
I'm amazed you didn't make a mistake =D. Got the identity matrix when multiplied those two together ^^
Shouldn't the det(a) =-3 ???
For matrix of minors, the element for row 1 column 3 is incorrect, right? it should be -1 instead of -2.
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 for all of your videos. Do you have any videos on the inverse of nonsquare matrices?
The left inverses that is.
more like matrix of minor annoyance... great video thank you from Canada
Good friends with the polynomial of partial inconvenience
YOU ARE AWESOME!!!!!!!!!
quick question... why did you calculate the matrix of minors?
why didnt you straight away calculate the det|A| and then the adj
Fantastic sal...
This 3 by 3 matrix is eating my brain away 🤯 But I’m learning so that’s good!!
Which Mathematician had come up with this idea?
Oh... my... GOSH!!! I UNDERSTAND MATH!!!