How to Find The Determinant of a 4x4 Matrix (Shortcut Method)

In this video I will show you a short and effective way of finding the determinant without using cofactors. This method is easy to understand and for most matrices is actually faster when you are good at row reduction. This method uses the properties of triangular matrices to quickly identify the determinant of a large 4x4 matrix. This video includes a worked example.

[@aylinahmedova1108]

Thank you!! My teacher expanded this in an unnecessarily complex manner but now I understand the concept

[@thepedzed]

Two rules are given, but there's a third important property of determinants: I. Row operation: has no effect on determinant II. Row swapping: negates the determinant III. Row scaling: multiplies the determinant by the scalar E.g.: A = B = [1 3 [1 3 2 2] 6 6] B: R₂ → 3·R₂, i.e. the scalar is 3, hence det(B) = 3·det(A). Check: det(A) = 1(2) - 3(2) = 2 - 6 = -4 det(B) = 1(6) - 3(6) = 6 - 18 = -12 det(B) = -12 = 3·det(A) = 3(-4) ✔

[@MrJona9999]

thanks:)

[@jessicarapier5330]

Well I'm going to go pass my final now. Thank you very much 😊

[@englishlife5838]

Thank you. That was super clear.

[@mendoxei1721]

Thank you so much for the simple and quick guide!

[@marinajacobo3550]

Thank you! This was helpful :)

[@nikolatancic3141]

tnx fast explanation right what i needed to refresh my memory

[@creatorofimages7925]

Very nice video for shortcutting the calculation.

[@jacobmatura5571]

Thank you for the good work.

[@crowbarenjoyer]

great video, many thanks!

[@52smritikumari14]

I really need this explanation....this is amazing......

[@albensmaine3057]

I really struggle with all my heart to understand Row and columns operations, it's just not obvious, I just can't see what operations to do, your's for example wasn't that hard, but the ones we do in class are just pure magic for me, how come everybody just instinctively knows what operations to do ? what am I missing ? a brain ?!

[@kwaitefuni9152]

The operations are arbitrary. You can pick whatever you like. R3 ->R3 + R1 (or something like that) The end result just has to be what you want it to be. Other than that, you can choose the operation yourself.

[@albensmaine3057]

@@kwaitefuni9152 i have reacted out of pure emotion on my last comment, i have now understood how to do it, as you said, i can choose the operation i want, and it's good to remind to the students that there are multiple operations you could do to,say, get the zeros for example.

[@kwaitefuni9152]

@@albensmaine3057 Great to hear that!

[@andresdubon1039]

you get used to it man, dont worry just practice. do you know what pivots are in matrixes? because once you know your pivot and turn it into 1, the rest is just easy stuff.

[@amlanbhuyan9761]

do some practice :). i am sure u will be able to this easily

[@ykd3529]

Thanks, this helped alot

[@explorenxaencantaja1093]

Very nice explanation..

[@khileshjaiswal]

Thank u ....it is very usefull trick ,I like it

[@heshanjalidilakshika2575]

Thank you so much!

[@yogesharora6032]

Thank you so much sir Sir, I request to you ,make a playlist of short tricks related with matrices

[@aysuoncu533]

thanks it helped a lot

[@elizabethessien4558]

very helpful

[@derrickwright1701]

Brilliant thanks

[@stormshadowsnakeeye8264]

Does the sign change when you swop again? I mean when you swop the 1st time, it changed from + to -. If you swop 2nd time, Does it changed from - to +??? Or it change the sign permanently???

[@iamlove1451]

as multiplying a raw with a constant is allowed, what if i multiply the second raw of the last matrix with 1/2 , that will change the pivot point to 1. that will change the determinant to 1*1*2*1= 2 . which is not equal to -4

[@Concon-bu4bp]

I'm not sure if this was mentioned but when I scaled a row it messed up the entire determinant. Keep in mind that scaling is sketchy lol

[@mentality1225]

Is this also applicable for complex numbers?

[@salizasaarisaari503]

if any row or coloumn of matrix A is multiplied by non zero k to produce a matrix B, then |B|=k|A|...my question is can this properties of determinant follow with divide by non zero k,then |B|=|A|/k ?

[@pauloalves5461]

Or use Laplace method to turn into a 3x3 matrix and solve by the default way

[@VelourChip]

How do you know when to swap the rows?

[@user-br2gu6xi8p]

i got u man

[@akshathanaidu7742]

what if we had to interchange the row/ column once again will the sign change to "+" ? '

[@theprocess2357]

Yes it will

[@uzairhussain4856]

Hello multiplying a row with scaler would change the determinant... Right?

[@taylor_h796]

Yes

[@dirojitkhersa3]

If we convert to lower triangular , do we get same result

[@jadejabrijrajsinh8610]

Yes.. As except for the first term ie a11 every term wil be 0 and taking the product of the diagonal elements will give you the determinant of the matrix

[@sahilrustamov2393]

thanks very much i understand OOOOKKKKKKAAAAYYYY

[@TheCompleteGuide1]

Glad it helped!

[@isonlynameleft]

Depending on the 4x4 matrix you get is this really that much of a shortcut?

[@Mieerxaa]

for 4x4 u can use this trick, I have use this trick and can be used in most of questions

[@H0peTladi]

Is it acceptable to use in the exam?

[@thanatosdriver1938]

yes unless they specify the method you need to use or if your particular teachers says not to. Worse yet if you were never supposed to have learned this in class email the professor asking if it's OK

[@blank_ec828]

will that method always yield to upper triangular matrix?

[@willgreg9020]

yes

[@trigocuantico]

always if the original determinant is non zero, we are always able to write a matrix in a diagonal form operating on rows and columns

[@patriknovak6264]

hello. Does this work for a n by n matrix?

[@programaths]

Yes, because adding one column to another doesn't change the determinant. Swapping negate it. And not shown in the video, you can also multiply a row by a scalar and the determinant will also be multiplied by that scalar. And everything that applies to rows ALSO applies to columns, because if you transpose a matrix, you keep the same determinant. (So, you could transpose your matrix, deal with its row, then transpose it again.

[@hewkarhao7323]

Why criss-cross method can’t be used to find the determinant of 4x4 matrix and above?

[@AayushSrivastava0307]

you can but very lenghyy youbhave yo solve 3 3x3 matrices as well

[@George_Nakhle]

God bless

[@blank_ec828]

where that formula comes from

[@trigocuantico]

the fact that there is a lower triangle of zeros annulates the effect of the determinant of all elements except the trace of the matrix. Try doing the determinant of a matrix like this the classical way

[@nomikhankhan6029]

sir i can use this method in every question.......... i mean when i solve the question then frst we convert it diagnol..........

[@unp2876]

@the complete guide WORKS FOR 3x3 .?./.!??

[@isaachiew4906]

yes it does

[@redguy5671]

What happens if you end up with a zero in the diagonal?

[@brian8653]

The matrix is singular

[@Mathematics-with-Waseem-Raja]

last Matrices How - sign 🙏🙏

[@user-tj7wd5em5z]

What if reading is not 1

[@bryansantiago302]

I tried this with different 4x4 with 3 attempts and every answer is different from each other.

[@mediaava]

I like it. Do you guys trust me

[@vandanakalokhe7224]

This is not shortcut.

[@thenaturefeeler381]

😂 yeh bhi sahi hai

[@infinitygamer8274]

Terai pass answer hai (do u have shortcut to it?)

[@SethStevens-xr7po]

If you are required to find the determinant of anything larger than a 3x3 matrix, this is definitely a shortcut.

[@peterpaul4347]

Which kain thing is this very hard to comprehend and totally confusing at the same time hmmm

[@ivynimer6053]

do u multiply the diagonal or do u add

[@safwansiddiqui7061]

Multiply, if you add you'll get 6 which is wrong

[@guillermogu5523]

This is fucking confusing!

[@lunatuna5203]

Thanks for the fucking ads

[@sivanand.b4474]

Its common method.. There's nothing like trick in this 🙁

[@adoomyforever3673]

This is a shortcut method, dont talk when you dont know shit.

[@chimchimmm4477]

its a trick hence your prof will never teach this in class but will rather want you to use those hectic steps to get to the same answers.

[@isonlynameleft]

I guess the trick is knowing the common method 😄