Simpler 4x4 determinant | Matrix transformations | Linear Algebra | Khan Academy

[@danholocaust7364]

KZbin is a better friend than teaching books!

[@PenandPaperScience]

If you want more practice, I upload 2 videos a week where I solve mathematics exercises step-by-step. The latest is solving a 4x4 determinant using another method that he does here. Perhaps it helps to give you more insight :)

[@daniboy2619]

Nope.

[@mesumabbas9481]

@@PenandPaperScience Chalo Bhai apni dukan na chamkao

[@taekwonwelchify]

its 12:30 am, i got my test at 8 am, and i COULD NOT figure out where those negative's (from swapping rows) were coming from... id be doomed without this video, thank you!!!

[@EngineerPrepper]

Perfect explanation, precise and to the point.. .Great Job!

[@2012INC]

I LOVE YOU SO MUCH! Why is this incredibly simple method not taught in maths lectures?

[@abdulnasif5551]

Man I am watching in 2024 ,now this video is like 14 years old but i cant explain how helpful it was to me.. thank you

[@Beskhuepnm]

You could try to get the matrix into a form where only 1 row starts with a non-zero number. Then, you calculate the dertiminant of this new matrix, which is just a constant times the determinant of the 3x3 matrix you get, which is pretty easy to calculate.

[@philipgao7648]

What if you interchange rows more than two times? Does that mean every time you swap two rows you get a negative sign?

[@mensaswede4028]

Yes, you are correct.

[@jeffreymelanson4549]

Very useful in solving eletrical circuits. Thx.

[@Amanijamac]

the guy is famous now, he is involved on how companies and schools help kids improve middle and high schools, he is kinda like education consultant in high rank, so :D

[@murtez22]

the great thing is when someone explain difficult idea in simple way in only a few minutes I mean seriously wow 🐸😱this was amazing

[@sfkc1588]

Ah that's what my teacher was talking about. The only words I picked up were triangle, zero and matrix but now I know what to do. Thanks!

[@MismeretMonk]

My best math teacher is KZbin :)

[@MarreLirre]

Thank you so much!

[@niFeforever]

Well this method is only useful with matrices which were intentionally made to be easily solvable, I mean good luck using this method in this 4x4 (54, 46, -85, 156), (-23, -2, -121, -69), (-61, 203, 40, -183), (16, 12, 1, 48), the answer is 0 btw.

[@xjpwcnm]

LOL

[@nillerh8236]

Well it is still "easy". You can always scale and use row interchange, just remember the steps you made later on when you have to calculate the determinant.

[@duchoang1074]

Using the expansion of cofactor may reduce the struggle I guess, since we will have 3 * 3 nest matrices to find its determinant. But for 5 * 5 or above, I think this "upper and lower triangle" option is more likely to be applied.

[@zeroanims4113]

the answer is 2919294

[@d7ooomymc346]

Kenneth Usares correct

[@FawazBnMohammed]

to save your time 3:25

[@waynesaviour]

hey bigman you seem to know evrything. from economics to accounts etc. who are you really?

[@ARNAKLDO]

He is the all-knowing fatha

[@cindermere3559]

batman

[@stutistuti2369]

Son of an INDIAN mother

[@div_yam2304]

he has 3 MIT degrees bro

[@mesumabbas9481]

Thanks it helped. Next day after tomorrow is my paper.

[@viktorbarsukov2894]

is that the ultimate question to Life, the Universe and Everything

[@vigabwoynetwork]

Today is 31 August 2023. I have an exam today this video has really helped me.

[@shiningyrlife]

@enjoyablesounds according to him, when u change row, the determinant of the matrix after changing is negative of the determinant of the matrix before changing row. That why u put a minus sign.

[@ershodyusupov9344]

Just greaaat!

[@alialiyev7324]

u are best teacher. u know this job ,man! thank u for explaining.

[@COKEDUDEUSF]

Is there a trick to calculating this one in upper triangle form? I got -114 as my determinant. 1,2,3,4 -1,4,6,4 1,2,1,1 1,-1,1,-1 I'm not sure if I did this step right. I multiplied the third row by -5/2 and added it to the fourth row. 1,2,3,4 0,6,9,8 0,0,2,3 0,0,5,-2 This is what I got 1,2,3,4 0,6,9,8 0,0,2,3 0,0,0,-19/2 And finally 1*6*2*(-19/2)= -114 I easily got the right answer from getting zeroes on 3 of the 4 entries in the first column. It was 57.

[@justindza]

This took me a little while but using a row 1 will put a nonzero in the 1st column, 4th row. Which will take away from putting in reduced row echelon

[@LadyAlchemy94]

YOU SAVED MY LIFE

[@noypathoumma9768]

โอ้​ ใครทำ​ sub thai เนี่ย​ ขอบคุณมากๆค่ะ!

[@navatagames]

This is really good sir. Thanks a lot for your tutorials

[@Marauder201]

When you flip rows you add a negative, but if you flip some rows again, do you cancel the negative (add another negative)?

[@ІванПилипко-у9с]

And can you actuallx flip other rows as well?

[@chom9993]

Thank you!!!!

[@Shvertz]

You are epic! Thank you so much!-

[@이재형12]

You saved student in Korea

[@sulthananajeeb3738]

beinging maths studying is well good for studying the matrix study easy to well understanding super experience fot students

[@sanamsanamrani6206]

Please use white board because iss say sei nazer nhi aitia

[@siva-ok9qk]

Thanks you very much :)

[@geemithafernando]

Wow.ur awesome man.love ur vids

[@AbdelaazizHESSANE]

Thank you :)

[@prasanthpentakota62]

Thank you

[@andregascoigne]

fantastic - thanks heaps :D

[@tusharvaswani2285]

Brilliant one

[@ebsanu]

great vid man. Are you a teach, if not you really should be.

[@anezkalascakova]

Is it working everywhere, or just on special types? For example, matrix like 1.row (1;2;1;-2), 2.row (0;2;1;2), 3.row (-1:3;1;3) and 4.row (-3;4;3;2), the determinant should be 22, but i cannot get that answer. Thanks

[@Flake4kv]

i dont want to insult u but u and math are two different worlds......

[@myonlynick]

video number 82 in the playlist describes the Sarrus rule. So, a 4x4 could be reduced to a set of four tables 3x3. Then, i suppose you could apply the Sarrus rule. It will be a hairy,long,not time efficient mathematical expression though. Yet easy to deal with

[@DanielSantoAngel]

Hey guys, check out this app, it computes the determinant of any matrix from 2x2 to 7x7 and it can make up matrices so you can practice!

[@ItzDaTwiGGajD]

thank you!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[@starwolf2125]

This reminds me of Gauss

[@bahaatamer1245]

I guessed that too at the beginning... :P

[@dalran5635]

So is it Jordan?

[@gaeagarcia3130]

wish this would work on variables

[@cuk2uk]

ur the best thx -.-

[@aljonloveiguibone]

U can't use this when one of the said diagonal is zero...

[@Hreinn91]

What happens if you swap two rows twice? Does the minus then cancel out? :-)

[@tiagovaladares2616]

yes

[@leezhijiang]

Can anyone explain to me how he came up with the way to make the lower part all zero ? 2nd row minus first row, then 3rd row minus 2 times the 2nd row ? How he came up with the ways ?

[@rioperez2115]

Fundamentals of matrix.

[@XperienceGames]

you are help

[@enjoyablesounds]

I don't understand why you wrote a minus after the row exchange..If i'm not mistaken you are just old fashioned row reducing right? Or is it a standard rule that when figuring out determinants you must switch signs when exchanging rows?

[@ІванПилипко-у9с]

4:27 have you just mistaken 4 to 2 or do i not get something right?

[@giobuta]

4:10 you need to say: third row minus two times first row, not second row. thanks

[@Randomxnames]

Gio Vardosanidze this videos been our for 10 years lmao

[@99crt]

ty............................

[@pierrefabela]

Sal stays savage

[@TsarKoragg]

There is a mistake det(kA)=k^n*det(A)...where n is order of the squate matrix. So, the answer will be (-1)^4*det(A)...thus answer is not -42 but only 42.

[@Uncertaintycat]

Why was R_2 X R_3 performed instead of R_4 X R_2 ? Usually you use partial pivoting and use the largest absolute value for swaps to avoid subsequent round off errors. Also R_3 has 0,3,1,0 when you swap and already contains a pivot at 1, so it means one less flop..

[@NightmareCrab]

nice

[@pzr17]

at 6:56 to make the 6 in the last row 0, why cant you perform this operation (-3R1 + R4). When I did this i ended up with the final answer as 36.

[@Bunny99s]

Uhm when you do R4 = R4 - 3R1 your new R4 would have a "-3" in the first column since the first row has a 1 in the first column. Once all rows have a 0 in the first column except the first row you can't use R1 for anything as every operation would change the 0 in the first column to something non-zero.

[@misstamanna2098]

Sir..! In the video, at time 4:29, in the 3rd row and 3rd column, the element 1 will not come..! [5-2*4]= -3 Isn't that...?? 😟

[@priyadharshinijayakumar9173]

he is subtracting row3 and 2times row1

[@abeerharoon2814]

How come the determinant is -42 and not 42. Considering when flipping rows, what I understood was that the determinant of the now new matrix is negative of the original matrix Am I missing something here? Cheers, thank you for all the help!

[@easymath643]

Me to I found the determinant 42

[@AJDIV93]

yup

[@listless32]

Are we able to switch/flip the Row 1 with Row 3? Not with this problem in particular but others.

[@dinadina5982]

yes you could after 5 years 🌚

[@ІванПилипко-у9с]

@@dinadina5982 what do you mean? Please state if that's possible or not

[@naomilouise1540]

If you get a matrix of lower triangular form, is the determinant still the product of the diagonal? :)

[@kumarraman8252]

At 7:10 why don't we multiply 3r row by 4th row ???

[@gurulinggbiradar6982]

after 4th transformation simplifying further is overkill

[@Ch1mp90]

Nice stuff! If I'm correct, than this is the same method that's used in the Gaussian Elimination method, right? Anyways, a huge thank you for this vid, my ass is saved :D

[@abandarolex395]

Is the determinat the sane as nature?

[@Rand0mDeath]

I don't get why he puts minus signs when switching rows....I usually never put them before. Do you have to put them only when you find determinants???

[@matthewolujic3923]

does this work for 2x2 matrices?

[@moodyabd]

So, if we swap rows twice does the sign stay the same?

[@ІванПилипко-у9с]

Logically, yes

[@conti_dumelo5545]

you said we replace the third row with -2x the 2nd row but you multiplied with the first row

[@maryamdiallo3613]

You said ' R3-2*R2' but subtracted row 3 from row 1...

[@jamoi2007]

how do you know when you are finished? because i have my 4x4 matrix and have the right numbers down my diagonal once i've put it in upper triangular form but some are the wrong sign (I am trying to calculate eigenvalues).

[@darkakib]

can u use dis technique for 5x5 matrixs

[@lesliemafuta4632]

Does this also work on 3*3 matrices ?

[@ibrahimelkhayyat7982]

If we swap two lines, the sign of the determinant flips aswell. Is this only for triangular form? Or does it have a specific rule?

[@Bunny99s]

This is a general rule for the determinant. Just think about a 2x2 matrix a b c d The determinant is (a * d) - (c * b) If you swap the lines you basically swap the terms so it becomes (c*b) - (a*d) which is the same as -((a * d) - (c * b)) The same logic applies to larger matrices but it's not that obvious in a 3x3 or 4x4 matrix. For a 3x3 matrix we usually just use the rule of sarrus: m00 m01 m02 m10 m11 m12 m20 m21 m22 det = +m00*m11*m22 + m01*m12*m20 + m02*m10*m21 - m20*m11*m02 - m21*m12*m00 - m22*m10*m01 m00 m01 m02 m20 m21 m22 // swapped m10 m11 m12 // swapped det = +m00*m21*m12 + m01*m22*m10 + m02*m20*m11 - m10*m21*m02 - m11*m22*m00 - m12*m20*m01 If you look carefully you will notice that the positive terms of our second matrix where we swapped two lines are actually the negative terms of the first matrix. If we re-arrange the terms of the second matrix to match the terms of the first we get det = -m00*m11*m22 - m01*m12*m20 - m02*m10*m21 + m20*m11*m02 + m21*m12*m00 + m22*m10*m01 As you can see all signs have flipped. So extracting a minus sign we get det = -(m00*m11*m22 + m01*m12*m20 + m02*m10*m21 - m20*m11*m02 - m21*m12*m00 - m22*m10*m01)

[@johndafish7829]

This technique is not reliable and does not always work. Example try and do it with this 4x4. 3,2,-1,0 0,2,0,1 1,-1,3,3 2,0,1,0 answer is -25 Its better to use the long way just to be sure. Especially during an exam.

[@Phantom_of_the_Oprah]

I know your comment is pretty old by now, and this reply is pretty late... But I calculated the determinant of the 4x4 matrix you gave with this method, and in fact I got the correct answer of -25. May be you made a simple mistake in your arithmetic... I'm not an expert, but I think this method is much faster, and much much MUCH more reliable than the other longer method of calculating smaller determinants. Try it again.

[@Phantom_of_the_Oprah]

Hi Tin, Here is my solution. If you have any questions, please let me know, and I will try to help. Please note that there is not just set set of steps that work, there are many sets of steps that you could take to reduce the matrix to a triangular form, which should give you the same answer. This is just the path that I took, trying to be as efficient as I can. Hope it helps. Eran.

[@Phantom_of_the_Oprah]

I emailed it to your google account. It shows as a comment, but doesn't show attachments. If you didn't get it, I can send it again. Or give me your email --

[@kardodasilay3020]

+Eran Amara I got the solution either but our instructor taught us different technique.

[@rioperez2115]

Got it, men.

[@chuaselo]

excuse Khan, what happens if you switch the 1st and last row. Do you still turn the matrix into a negative.?

[@amirulashraf3615]

everytime you switch row or line, the matrix will turn from + to - or - to +

[@Walid10105]

are you using so called Gauss-elinimination method?

[@Jakenbake98]

I FUCKING HATE THE NEW COMENT SYSTEM THERE IS SO MUCH STUFF MESSED UP WITH IT UGH

[@chrislam1341]

which video did u explain swapping the rows have to add an negative sign? I am impressed with your explanation and wanna explore some more :)

[@khineyinmon9323]

www.khanacademy.org/math/linear-algebra/matrix-transformations/determinant-depth/v/linear-algebra-upper-triangular-determinant?LinearAlgebra&Desc&YT www.khanacademy.org/math/linear-algebra/matrix-transformations/determinant-depth/v/linear-algebra-determinant-after-row-operations?LinearAlgebra&Desc&YT

[@d4ncy1]

is there a faster method to do this by any chance?

[@caiosm1005]

@mybrotherstolemypen yes

[@alias40anon]

Excellent videos , thanks. By the way when this guy pronouncing vowels he reminds me Stewie Griffin from family guy hoho

[@samsquires5246]

you da bomb

[@JakkuSakura]

Can't thank you more

[@LoveofGiraffes]

is this also called the gussian method?

[@Locksock27]

Is this Cramers rule

[@bahaatamer1245]

I have some questions out of this video... Some things you did here have no proper explanation, like swapping the rows (I'm pretty sure some swaps will give different answers)

[@Bunny99s]

No, it doesn't matter which rows you swap or how often you swap as long as you always flip the sign when you swap two rows. It's highly recommended to only do one step at a time. So if you want to do two different swaps it's better to perform them one after another.

[@dreamlanddon]

can I use this method for a 3X3 matrix? It seems that this doesn't work well.

[@MrBarca154]

dreamlanddon yes you can :)

[@santalos5]

How many times can you swap? And can you swap any row?

[@seankelley1216]

He multiplied by the wrong #, The Determinant is -26

[@onothodox]

Explain

[@LadyAlchemy94]

you sound like tom hanks btw :D

[@ST-us7kq]

can i do it by making it lower triangular?

[@jamesy0117]

yes but getting a matrix into echelon form, which implies upper triangular, is much easier using algorithms

[@Thipok30386]

Does it really works? Its looks too easy...

[@00GumbieNF00]

how do I know which row to plus minus etc.. @.@

[@myshowTM]

Now hold the phone... I thought multiplying a row by a scalar C also scales the determinant by C... SAL!