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

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Calculating a 4x4 determinant by putting in in upper triangular form first.
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[@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

[@2012INC]

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

[@EngineerPrepper]

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

[@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!!!

[@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.

[@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

[@alialiyev7324]

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

[@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!

[@navatagames]

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

[@MarreLirre]

Thank you so much!

[@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.

[@jstdun]

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

[@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

[@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

[@MismeretMonk]

My best math teacher is KZbin :)

[@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

[@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

[@Shvertz]

You are epic! Thank you so much!-

[@chom9993]

Thank you!!!!

[@andregascoigne]

fantastic - thanks heaps :D

[@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

[@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.

[@sulthananajeeb3738]

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

[@LadyAlchemy94]

YOU SAVED MY LIFE

[@mesumabbas9481]

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

[@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.

[@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).

[@gaeagarcia3130]

wish this would work on variables

[@starwolf2125]

This reminds me of Gauss

[@bahaatamer1245]

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

[@dalran5635]

So is it Jordan?

[@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..

[@viktorbarsukov2894]

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

[@noypathoumma9768]

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[@safirana3814]

Thank You So Much!!!

[@geemithafernando]

Wow.ur awesome man.love ur vids

[@AbdelaazizHESSANE]

Thank you :)

[@vigabwoynetwork]

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

[@alias40anon]

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

[@siva-ok9qk]

Thanks you very much :)

[@tusharvaswani2285]

Brilliant one

[@naomilouise1540]

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

[@ljh00]

You saved student in Korea

[@prasanthpentakota62]

Thank you

[@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?

[@ItzDaTwiGGajD]

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

[@aljonloveiguibone]

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

[@user-uh1xh4dq3q]

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

[@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)

[@pierrefabela]

Sal stays savage

[@cuk2uk]

ur the best thx -.-

[@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!

[@FawazBnMohammed]

to save your time 3:25

[@conti_dumelo5545]

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

[@XperienceGames]

you are help

[@ershodyusupov9344]

Just greaaat!

[@Marauder201]

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

[@user-uh1xh4dq3q]

And can you actuallx flip other rows as well?

[@matthewolujic3923]

does this work for 2x2 matrices?

[@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.

[@ebsanu]

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

[@darkakib]

can u use dis technique for 5x5 matrixs

[@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

[@vincentfiestada]

So if I do an even number of swaps, the determinant will not change?

[@pierrefabela]

pretty much

[@Walid10105]

are you using so called Gauss-elinimination method?

[@Hreinn91]

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

[@tiagovaladares2616]

yes

[@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???

[@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

[@LoveofGiraffes]

is this also called the gussian method?

[@d4ncy1]

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

[@lesliemafuta4632]

Does this also work on 3*3 matrices ?

[@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.

[@LadyAlchemy94]

you sound like tom hanks btw :D

[@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.

[@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

[@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 🌚

[@user-uh1xh4dq3q]

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

[@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 +

[@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

[@dreamlanddon]

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

[@MrBarca154]

dreamlanddon yes you can :)

[@moodyabd]

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

[@user-uh1xh4dq3q]

Logically, yes

[@kumarraman8252]

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

[@doomguardex1]

The equation is lifting off lol

[@gurulinggbiradar6982]

after 4th transformation simplifying further is overkill

[@99crt]

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

[@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

[@abandarolex395]

Is the determinat the sane as nature?

[@samsquires5246]

you da bomb

[@maryamdiallo3613]

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

[@Flake4kv]

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

[@NightmareCrab]

nice

[@caiosm1005]

@mybrotherstolemypen yes

[@AJDIV93]

yup

[@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

[@TheTrueMilery]

damn, so close to being 1337 :P

[@00GumbieNF00]

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

[@sanamsanamrani6206]

Please use white board because iss say sei nazer nhi aitia

[@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.

[@myshowTM]

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

[@santalos5]

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

[@RICExCRISPY]

it.all.makes.sense.now. :D!!!!!!!!! My teacher is just plain horrible when it comes to this stuff. thanks so much!

[@inkiyadrahman57]

Is this Cramers rule

[@seankelley1216]

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

[@onothodox]

Explain

[@Thipok30386]

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