n x n determinant | Matrix transformations | Linear Algebra | Khan Academy

Defining the determinant for nxn matrices. An example of a 4x4 determinant.

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[PaperBagMan]

Thanks! I wish my professors were as fluent in teaching as you are.

[cheerfultrout]

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.

[globotron]

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!

[jacobsilcoff]

This video was really helpful for my comp sci class. Thanks so much!

[GodofMind]

have an exam tommorow ..
Dosent matter you there ! my savior thank you !

[moghimiiman]

final exam in the next 3 hours, thanks :-D

[oxymon]

Hoooly shit, you just gifted me with the ability of enjoying the beauty of math! Thanks dude!

[yeetelite]

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.

[rengstrom]

Wow, I actually get it! First math teacher who actually taught me anything! :P

[mensaswede]

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.

[melikaarshadi]

Great video! Thank you. I'm just wondering why you switch sides with minus, so you suddenly do an addition?

[mensaswede]

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.

[dilly]

thank you so much, this is brilliant, it made such an impact!

[kylahvatum]

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.

[Kevin-jmgo]

This video is almost 100 years old, but it's still gold

[epgmw]

Thanks a lot, very helpfull indeed. Keep up the good work

[TheBullyNgitPangit]

sir.Khan at the yellow color 0-9 why u didn't multiply (-2 | -9)

[georgethemagiclamb]

Thank you! Very helpful and straightforward.

[dbmasters]

Multiplying by 0 is the shiznit.
Sal, you rock as usual.

[milanvagner]

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.