I noticed while I was watching that the recursive rule also applies to a 2x2 matrix. therefore I would argue that even more fundamental than the definition of the determinant for a 2x2 matrix (7:55) is the determinant for a 1x1 matrix, which is itself. (and the recursive rule can also be applied to the 2x2 matrix in this way) It's the same thing really, just thought I'd point it out for people like myself, for whom looking at it like this makes it easier to understand/remember.
It's not that the recursive definition "applies" to a 2x2 matrix, it's that the 2x2 fits into the general definition. Think about the *ad-bc* for the 2x2 determinant as just a practical device so you don't have to use the definition. Kind of like a "cheat" formula.
great for nontraditional students who didn't do this stuff in high school. I need these things "dumbed down" (I mean that in the most respectful way). Thanks for the help!
I found [+|-] at the bottom of the Wikipedia page "List of mathematical symbols", it's called situational plus or minus in case you want to be really specific about the sign depending on the size of the matrix.
Actually the 2x2 case can use the recursive definition also. If you just define the determinant of a 1x1 matrix as the value of the single entry, then the 2x2 matrix reduces using the recursive definition to the sum and difference of the top row entries plus/minus the determinant of the 1x1 sub-matrix.
Looking at the comments, it seems the only way some people would understand is if you did motion animations showing the sub-matrices appearing from the original matrix. I bet the light bulb would go on. Because it actually is pretty simple, but hard to show by hand drawing.
Great video but now i have the task to count the determinant of an nxn matrix. We dont know how many columns and rows are in the matrix but still i'd be expected to give a strict answer (number). Im sure some tricks can be figured out in these kinds of excercises but so far i couldnt do them. Please let me know if you know about any tutorials of similar excercises on youtube.
In the second submatrix you multiplied -6 by two twice. (0x0)-(2x3) = -6 which is correctly stayed but you multiplied it by two and put it into the formula to multiply it by a 2 again. I hope that makes sense… unless I am misunderstanding the procedure. This can be noticed at the time 16:11 and on.
Lol I tried solving this via transforming it into an triangular matrix and then just taking the determinant by calculating the product of the primary diagonal elements. Turned out that I copied a number wrong and I kept wondering if I have done anything wrong since my determinant always became 0. :D I also once used Laplace to calculate the determinants in some homework. Turned out I've forgotten about basic determinant rules and so I calculated the easiest stuff with the most difficult way.
Cool, I was making a Class Library in C# for matrices and needed a method for determining the determinant. It was much easier than I originally thought it would be to implement (because of recursion). Sal, you should do some Computer Science videos. I'm tired of everyone asking me to tutor them.
Because of dimensionality. The dimensions are like you hands, your left hand is the inside out of your right hand. Think of a glove! Hence the negative
Why is the sound gone both for videos I watch of Khan and PatrickJMT? All other youtube videos have functional sound! Why must it target the two math gurus when I am in the most of need?? :(
What you say around 0.42 second about changing the sign of a_12 may not be correct! My book says differently. Could you please check this part! For instance for 3x3 matrix, D(A)=a_11A_11+a_12A_12+a_13A_13. Capital As are the cofactors.
u can only invert a square matrix, determining the determinant of a 2xn matrix isn't defined. U can only have determinants for 1x1, 2x2, 3x3 4x4... etc matrices
the determinant is of a 1x1 matrix is just the value what's inside the 1x1 matrix, that's just defined. for example: the determinant of [12] is just 12, so the inverse of A=[12] is just A^-1=[1/12]
Looking at these comments before me made me wonder "hm.. maybe my profs were in the same spot as I am now 10 years ago and looked up this video as well"
4 years ago, but I'll reply incase it can help others. You take 1 / the determinant and then times it by the augmented matrix. If the determinant is 0 that means 1 / 0 = 0 and if you time the augmented matrix by 0 then it also becomes 0. So in a way you could say that if the determinant is 0, the inverse of the matrix is the empty matrix, but that sounds kind of weird :P
What wasn't explained is why this recursive formula was the chosen definition. Why did you have to switch signs for every row? I'm amused how people just accepted this and felt like they know perfectly what's going on 😆
Derick Pinkerton Lol u little turd, r u even capable to understand a joke? And ur answer is yes, i m 20, i m in mathematical analysis, this stuff is for 17 yo people
┌ ┐ │ aₙ ₙ aₙ ₙ₋₁ ⋯ aₙ ₁ │ │ aₙ₋₁ ₙ aₙ₋₁ ₙ₋₁ ⋯ aₙ₋₁ ₁ │ │ ⋮ ⋮ ⋱ ⋮ │ │ a₁ ₙ a₁ ₙ₋₁ ⋯ a₁ ₁ │ └ ┘ So I had an idea for using less wording, but now it's now turned into a question. When defining a reverse n x n matrix, would the first element still be a₁ ₁ or aₙ ₙ? Does the order flip along with the matrix indexes?
Thanks! I wish my professors were as fluent in teaching as you are.
i wish mine too:)
I noticed while I was watching that the recursive rule also applies to a 2x2 matrix. therefore I would argue that even more fundamental than the definition of the determinant for a 2x2 matrix (7:55) is the determinant for a 1x1 matrix, which is itself. (and the recursive rule can also be applied to the 2x2 matrix in this way) It's the same thing really, just thought I'd point it out for people like myself, for whom looking at it like this makes it easier to understand/remember.
👍
It's not that the recursive definition "applies" to a 2x2 matrix, it's that the 2x2 fits into the general definition. Think about the *ad-bc* for the 2x2 determinant as just a practical device so you don't have to use the definition. Kind of like a "cheat" formula.
have an exam tommorow ..
Dosent matter you there ! my savior thank you !
This video was really helpful for my comp sci class. Thanks so much!
great for nontraditional students who didn't do this stuff in high school. I need these things "dumbed down" (I mean that in the most respectful way). Thanks for the help!
final exam in the next 3 hours, thanks :-D
did you pass?
Mine in next 4 hours , and iam scared as hell :D
What year in bachelor? Maths or CS or ?
@@zenchiassassin283 you'll never know
@@celeryystick lol
Hoooly shit, you just gifted me with the ability of enjoying the beauty of math! Thanks dude!
Great video! Thank you. I'm just wondering why you switch sides with minus, so you suddenly do an addition?
Thank you! Very helpful and straightforward.
Great, how would you code this on matlab using recursion.
I found [+|-] at the bottom of the Wikipedia page "List of mathematical symbols", it's called situational plus or minus in case you want to be really specific about the sign depending on the size of the matrix.
Wow, I actually get it! First math teacher who actually taught me anything! :P
you are an angel from heaven
thank you so much, this is brilliant, it made such an impact!
I was about ready to drop out but now it all makes sense
Actually the 2x2 case can use the recursive definition also. If you just define the determinant of a 1x1 matrix as the value of the single entry, then the 2x2 matrix reduces using the recursive definition to the sum and difference of the top row entries plus/minus the determinant of the 1x1 sub-matrix.
Multiplying by 0 is the shiznit.
Sal, you rock as usual.
This video is almost 100 years old, but it's still gold
O'boy, I can't wait to do these computations!
Thanks a lot, very helpfull indeed. Keep up the good work
Okay... The introduction to matrices and multiplation is enough for me for today...
still informative. thankyou
Looking at the comments, it seems the only way some people would understand is if you did motion animations showing the sub-matrices appearing from the original matrix. I bet the light bulb would go on. Because it actually is pretty simple, but hard to show by hand drawing.
Quiz tomorrow, thanks for your help!
Great video but now i have the task to count the determinant of an nxn matrix. We dont know how many columns and rows are in the matrix but still i'd be expected to give a strict answer (number). Im sure some tricks can be figured out in these kinds of excercises but so far i couldnt do them. Please let me know if you know about any tutorials of similar excercises on youtube.
that was awesome
sir.Khan at the yellow color 0-9 why u didn't multiply (-2 | -9)
can we write the general expression of determinant in a very useful form?
amazing! thank you!
sal why dont you teach me the math behind electromagnetics. could sure use your help there haha
Thank you so much!
I see a previous exam is computing a 6x6 without a calculator, is it really that bad? Seems really time consuming, even if you understand it.
thank you Sal you are amazing
This is really AWESOME !!!💋
In the second submatrix you multiplied -6 by two twice. (0x0)-(2x3) = -6 which is correctly stayed but you multiplied it by two and put it into the formula to multiply it by a 2 again. I hope that makes sense… unless I am misunderstanding the procedure. This can be noticed at the time 16:11 and on.
THANK YOU SO MUCH!!!!!
which software do u use in this lesson and other lessons? +Khan Academy
Thank you so much.
what about that formula?
Lol I tried solving this via transforming it into an triangular matrix and then just taking the determinant by calculating the product of the primary diagonal elements. Turned out that I copied a number wrong and I kept wondering if I have done anything wrong since my determinant always became 0. :D
I also once used Laplace to calculate the determinants in some homework. Turned out I've forgotten about basic determinant rules and so I calculated the easiest stuff with the most difficult way.
sal u should post videos for computer science major !!!!!!!!
Cool, I was making a Class Library in C# for matrices and needed a method for determining the determinant. It was much easier than I originally thought it would be to implement (because of recursion). Sal, you should do some Computer Science videos. I'm tired of everyone asking me to tutor them.
frickin awesome dude
But why are we changing signs???)
Because of dimensionality. The dimensions are like you hands, your left hand is the inside out of your right hand. Think of a glove! Hence the negative
thank you so much
Why is the sound gone both for videos I watch of Khan and PatrickJMT? All other youtube videos have functional sound! Why must it target the two math gurus when I am in the most of need?? :(
you save my life
i appreciate your vids : )
damn my brain wanna explode!!
would this work the same if there were negative coefficients?
RazorX53 Yes, you just need to be careful about the signs.
Very useful
Finally!!! I swear my linear algebra teacher sucks. 20 min on CZcams is better than an 1hr of lecture.
I love you man!!!!!!
Thanks!
u rock!
What you say around 0.42 second about changing the sign of a_12 may not be correct! My book says differently. Could you please check this part! For instance for 3x3 matrix, D(A)=a_11A_11+a_12A_12+a_13A_13. Capital As are the cofactors.
God bless you dude I really mean it ! =)
How about the determinant of a 2 by n matrix which won't have a basic (ad-bc) when you ignore the first row.Then, how do you do it?
u can only invert a square matrix, determining the determinant of a 2xn matrix isn't defined. U can only have determinants for 1x1, 2x2, 3x3 4x4... etc matrices
Pekky thank you but that is the deterninator of a 1x1 matrix?
what do you mean? do you mean what the determinant of a 1x1 matrix is?
Pekky ya because you can't do the ad-bc so you can't find the inverse
the determinant is of a 1x1 matrix is just the value what's inside the 1x1 matrix, that's just defined. for example: the determinant of [12] is just 12, so the inverse of A=[12] is just A^-1=[1/12]
Looking at these comments before me made me wonder "hm.. maybe my profs were in the same spot as I am now 10 years ago and looked up this video as well"
but why is it that the determinant results in the same value regardless of the row or column from which it is expanded
But why does this work? I mean, why does when the det=0 when calculated this way makes the matrix not invertable?
4 years ago, but I'll reply incase it can help others. You take 1 / the determinant and then times it by the augmented matrix. If the determinant is 0 that means 1 / 0 = 0 and if you time the augmented matrix by 0 then it also becomes 0. So in a way you could say that if the determinant is 0, the inverse of the matrix is the empty matrix, but that sounds kind of weird :P
What wasn't explained is why this recursive formula was the chosen definition. Why did you have to switch signs for every row? I'm amused how people just accepted this and felt like they know perfectly what's going on 😆
the cramer method is fastest way of getting a 3x3
I wish I could see some demonstration or deduction of the formula.
You can derive it yourself from the definition of A inverse
thank you so much, finally I understood matrices
*Matrix
Eddy Seid Matrices* lol are you even in linear algebra?
Derick Pinkerton Lol u little turd, r u even capable to understand a joke? And ur answer is yes, i m 20, i m in mathematical analysis, this stuff is for 17 yo people
Eddy Seid 20 years old and doesn't know how to speak English? Khan has videos on English grammar too I suggest you watch a few
Great,
yea, QQ some more like you know his algebra teacher
How we solve matrix more than order of 4 , 5,6,7 etc
This is Cofactor expansion?
No.
nice
so it never simplifies?
┌ ┐
│ aₙ ₙ aₙ ₙ₋₁ ⋯ aₙ ₁ │
│ aₙ₋₁ ₙ aₙ₋₁ ₙ₋₁ ⋯ aₙ₋₁ ₁ │
│ ⋮ ⋮ ⋱ ⋮ │
│ a₁ ₙ a₁ ₙ₋₁ ⋯ a₁ ₁ │
└ ┘
So I had an idea for using less wording, but now it's now turned into a question.
When defining a reverse n x n matrix, would the first element still be a₁ ₁ or aₙ ₙ?
Does the order flip along with the matrix indexes?
This is 4x4 det.
Where is the nxn det.?
gauss-jordan elimination determinant anyone?
16:07 how is 2x3 = -6 ?
it's supposed to be 6. Then -2x6 = -12 and -2x(-12) = 24 is the final result of that part.
+MrAlpha545 Ow, ok I get it. Thx
i keep getting -7 and cant find my error, anyone get the same thing?
from Hyperlink?
u r not going to done 5x5 and 6x6 matrix question in 20 mins!
"We are afraid of what we don't understand." ... Well I guess you dont get this then ;P Haha naah just kidding :))) Cheeers maan!
Yes, but only because 1/0 is undefined.
you get, you get…..YOU GET
sorry i had to make a snarky comment, thanks for the help!
I know this is just the natural function of numbers and has no sentient quality to it whatsoever but somehow this feels evil...
How dare you insult your linear algebra teacher!