How to find the determinant of a 3 by 3 matrix (3 ways) linear algebra tutorial

[@Arrathix]

I really appreciated the calculus humour sprinkled throughout this lesson. Really made my day

[@adminguy]

6:09 Lastly we have plus C. We won't do integration so don't get too excited... (A few seconds later)... And then times the derivative of ...

[@not_vinkami]

9:12 the derivative of a 3 by 3 matrix Me, an intellectual: 0

[@blackpenredpen]

Lolll

[@danji9485]

wow I was just learning about matrices

[@brooksgunn5235]

Same, I just took a linear algebra test about this exact thing.

[@SimonClarkstone]

This time, the interpretation of determinant as the signed volume of a paralellepiped wasn't quite so useful. I haven't understood yet why the cofactor rule works geometrically, but I expect it'll come to me. However the adding of a multiple of one row to another row is clearly a skew that doesn't affect the volume, and the shape created by a triangular matrix makes it easy to calculate the base×height of a paralellogram etc. (Thanks again 3b1b for showing me that.)

[@faizansaiyed3349]

HOW DO YOU KNOW IM LEARNING LINEAR ALGEBRA

[@localtitans4166]

Thing to be thought 🤔

[@hunainaghai3342]

He's like ATHLEAN-X. knows everything already

[@ilickcatnip]

6:10 calculus enters the chat. And also "the derivative, no no, determinant of..."😂

[@Happy_Abe]

"It seems I'm the one who's getting excited" Haha I love you

[@garyhuntress6871]

I'm wearing my BPRP "Derivatives for you" tee shirt today!

[@blackpenredpen]

Nice!

[@PranavvSalunkhe]

The shortcut is called as "Sarrus Rule".

[@AbirInsights]

I know it as Expansion of sarrus diagram

[@Dalton1294]

I learned a little bit about matrices in pre calc and we were taught to write the 3X3 matrix to the right because the matrix wraps around itself. The teacher had 3X3 matrix on a piece of paper and rolled that paper into a cylinder to show us as a visual

[@Revolver03]

I literally started this today and now you upload, the timing

[@manik1477]

Its funny how the shortcut is technically longer than the cofactors

[@Apollorion]

About which method I liked the most: if I'd know before hand that the matrix will always be 3x3 as well as am a dumb but quick calculating computer I'd apply the shortcut method, but if the size is beforehand yet unknown, I'd try to make an algorithm to transform the matrix (by using the properties of determinant) into a triagonal matrix after which I only multiply the elements of the diagonal. Speeking of the latter, how about doing this: add the bottom row (i.e. [5 1 2] ) to the top row, thereby transforming this into 1 3 3 which we then subtract single and fivefold from the second and third row respectively, turning these into 0 -1 0 and 0 -14 -13 respectively which we can now easily compute by cofactor expansion over the first column to be 1 times (-1 times -13 plus 0 times -14) which again turns out to be 13 ? ... Or we could just substract 14 times the 2nd row from the 3rd, making the -14 disappear & thereby changing the matrix into a triangular, but nothing more, and the determinant just 1x-1x-13=13.

[@guillemllodra7304]

Using the properties of the determinant can also be solve quickly. First we need a column full of 1's, to get that multiply the last row by 2. | -4 2 1 | 1/2 | 1 2 3 | | 10 2 4 | Now, column 2 has a common factor 2, hence: | -4 1 1 | | 1 1 3 | | 10 1 4 | Then, leave row 1, and modify row_2 and row 3 as row 2 - row 1, row 3 - row 1, respectively. | -4 1 1 | | 5 0 2 | | 14 0 3 | Now, we can simply , do the cofactor expansion: -1 | 5 2 | = 13 | 14 3 | This strategy is quite useful, to reduce the number of computation in the cofactor expansion. Obviously, you need to find a quick way to make a full 1's column/row.

[@FrankyMelon]

thanks for the reminder... quite some time has passed since i learned that :D

[@kalkal8050]

Good poke-ball, it held me for 14:56 mins.

[@80天從零到台大]

Your video perfectly simplifies what my Taiwanese math textbook took several pages to prove and explain.

[@helo3827]

I am having a test on matrix tomorrow, your videos have improved my math grade! I wish you can do more videos on linear algebra. Keep it up

[@MrPanzerTanzer]

I hope the test went well.

[@helo3827]

@@MrPanzerTanzer I hope so too

[@nilaxibhoot2899]

🙏🙏I inspired learning maths seriously from you.

[@hotlatte1222]

Move so fast! Shortcut to score! Control a ball with left handed skills. OMG. This is the best highlight i have ever watched, of James Harden.

[@blackpenredpen]

LOL James Harden!

[@ianang8977]

The second method really reminds me of the shoelace method

[@sainandan5282]

What is shoelace method??

[@megauser8512]

I like the 2nd method the most!

[@DavesMathVideos]

Nice explanation for the proof of the shortcut.

[@blackpenredpen]

Thank you

[@ThomasTheThermonuclearBomb]

I really wish I saw this video yesterday because I could’ve used it on my exam. Great video!

[@nitayderei]

If you add to the last row the first and subtract the second, the last row is (0 1 0) so you can calculate it quite easily.

[@adrianmacias9144]

Dude you're amazing, you always upload math videos relating to the math class I'm taking lmao. First the integration videos with calc 2 and now the linear videos for linear algebra!

[@yassine321]

I am so excited for difficult linear algebra problems

[@zerovibritannia6216]

This topic is going to be included in my upcoming exam next week :)

[@XxPlayMakerxX131]

I forgot about that method where you repeat the first two columns. I miss when it was the only method I know to compute a 3x3 matrix... Thank you for the Great videos

[@lulekozikode3029]

Why do we have to multiply the determinant by -1 when we interchange rows?

[@blackpenredpen]

Notice the sign of the second row is the opposite of the first. See the red part. So when you interchange, you change the sign

[@fresh7995]

u dont really need to make it a triangular matrix if u can make it have 2 0s and a number (13:24) u can just find the det of the 2x2 and x it by the 1 or whatever other number u have. idk i feel like thats quicker

[@egillandersson1780]

You are greypenredpen, now ! 🤣 The third method is quite elegant. I didn't know it.

[@christophermusso]

At 13:37 you multiplied the 2nd row by 9/10, but next to the center 10 you wrote "9/10" in red instead of "9".

[@blackpenredpen]

Ahhhh thanks

[@ianmoseley9910]

Really discovered how much I had forgotten about matrices.

[@blackpenredpen]

Same here. I just started to pick up linear algebra again after many many years.

[@TobyBW]

Just so you know, you added a basketball video to the Hello Linear Algebra playlist.

[@blackpenredpen]

Loll my mistake. Thank you.

[@joaopedroalves1200]

@@blackpenredpen btw you also added a dbz video in the number theory playlist

[@MrPanzerTanzer]

Dont mind watching blackpen doing some dunks

[@jackkalver4644]

Apparently for large matrices, row operations work way faster than cofactors. But I know that once the order has been reduced to 4, you can compute six 2x2 determinant products and add them up.

[@vaishalishah4108]

Students of class 11 are taught this stuff and it is that basic. Will you please provide some challenging questions of this type?

[@seroujghazarian6343]

4:14 "2 times 1 times 1" 😂

[@poi_aithhkunnnRVC]

Pls do lagrange resolvent for high-degree equations.

[@SwordQuake2]

The second one is not just "the shortcut", it has a name (that I can't remember now).

[@kormosmate2]

Sarrus rule

[@knutritter461]

I can remember my maths for chemists at the uni... and I can remember those matrices! And I can remember the harassment with '-' with larger matrices :-D

[@chunfaimok767]

"The most difficult part would be calculating all the stuff with a calculator." Experience from a Hong Kong M2 student

[@mdabusayem8755]

First comment from Bangladesh 🇧🇩🇧🇩🇧🇩....love u brother❤ from Bangladesh🇧🇩🇧🇩

[@nisargbhavsar25]

Kemonachi, Bhalo? Love from India!

[@alistaw1866]

Im surprised how it ended up. That's so cool.

[@binaryblade2]

why would you work out the 13/10 fraction instead of adding rows 2 & 3 together because the 13s line up.

[@blackpenredpen]

bc we needed the -9 to be 0 so we could get an upper triangular matrix

[@binaryblade2]

@@blackpenredpen right, but you can swap columns 2 & 3 (taking another -1) and then it's triangular.

[@blackpenredpen]

Jonathan Fraser Ah yes! I didn’t see that.

[@MrRyanroberson1]

I always go for triangular. No exceptions! Though i won't always finish it before computing

[@abhilashgupta5934]

This method is great if you have to fill the sheets in your exam.

[@rkcoder]

Awesome! Linear Algebra and a new cool beard!

[@eugeneimbangyorteza]

I have always been using criss cross for 2×2 and 3×3 since forever

[@berzerksharma]

The shortcut is called rule of Sauras, read about it in Higher algebra by hall and knight

[@fcgod6017]

Sarrus rule*

[@connorhorman]

I never used the triangular matrix method, so my favourite is the shortcut. The former would definately be useful though

[@ziyilin2029]

How about doing that with vectors, normal vectors and also the volume?

[@vikneshs8662]

please make more linear algebra videos

[@eduardoponciano8007]

Muito bom cara. Vou entender o que você fala um dia. Vlw

[@anshulagrawal3931]

great thanks

[@easygoing1719]

On which 4x4 matrizes could you also use the shortcut similarly to 3x3 so that you end up with a correct answer?

[@Apollorion]

The ones in which 3x3 matrices are cofactors.

[@hocinlaggoun1413]

integral x/sqrt(x^2+x+2)

[@OnlyTheQuack]

Imo, that shortcut takes more time than judt using the cofactor since doing cofactord also gives u 1/3 of the Inverse matrix

[@neilshah3059]

How does the determinant change when you scale a row?

[@Apollorion]

As the comment of Guillem Llodrà has shown: the determinant scales that same factor with it & you need to compensate for it if you wish to achieve to find the exact same outcome, same goes for columns. If you only wish to find out if the determinant is equal to zero or not, you can of course ignore this influence.

[@snide1574]

That shortcut is also called sarrus method

[@cameronspalding9792]

I always use row reduction

[@deepabenjwal1507]

You are mind blowing

[@嘚嘚十八刀]

Why can interchange rows

[@mohamad2671]

perfect sir

[@lordshen3078]

this is part of clss 12 syllabus in india still a good video

[@Frederic7594]

Shortcut aka Rule of Sarrus

[@germangonzalez1080]

9:10 the derivative of a matrix... Big F

[@gonzalomorislara8858]

You actually can if it has variables in it!😃. It is called the jacobian and it is super useful in multivariable calculus

[@prateekmourya9567]

Will you keep the promise of making a video on Riemann hypothesis on reaching 1 million subs?

[@alainrogez8485]

I use Sarrus.

[@adrianparism]

In the third method you get -1 actually three times. The result is the same, of course, but I think it's important to specify that detail.

[@blackpenredpen]

I only interchange the rows one time tho.

[@anishadj6157]

Limit when x----->0 of exp(x^x) For fun 😊

[@helo3827]

why, you are uploading constantly, keep it up

[@8dolev]

9:07 Who is excited now?

[@hocinlaggoun1413]

Please integral x/sqrt(x^2+x+2)

[@deniseockey6204]

The first way was the way I learned. I am not sure about the third way. I will have to play with some other examples.

[@matty7834]

Anyone doing matrices in further maths in the UK?

[@omshandilya8888]

2020 raise to the power 2019 - 2020 divided by 2020 square + 2021=N then find the sum of digits of n bro plz solve this?? trying from last 5 weeks

[@adam_elm_5680]

Pls i need help Proof that for all x€R cosx + sinx =< square.root(2)

[@Alex-di9en]

Can someone help me with this problem: consider Fibonacci sequence: 1,1,2,3,5,......,An prove that for all n: A(n+1) < (7/4)ˇn

[@Lastrevio]

bro i already know all this shit i feel smart

[@ranjitsarkar3126]

He is obsessed with derivative 9:12

[@42-94]

By definition, maybe?)

[@Suraj-on7bf]

Hlo my name is Suraj and I am from India I want that u can prove the formula of arithmatic mean which is x=x1+x2+x3.......Xn/n

[@localtitans4166]

Ur beard looks new

[@JSSTyger]

Ugh...matrix algebra. Excuse me while I barf.

[@barkbarkbark198]

Woah a beard now lol

[@danji9485]

oh god the comments section turned into "first" hell

[@estelle_chenxing]

Hey #YAY

[@colleen9493]

First

[@danji9485]

shut up

[@chessematics]

Again that heck beard!!!!

[@peakpersona-yash]

Plz look my proof that 0¹=not defined So, 0¹ can be written as 0 to the power 2-1 Then by exponent rule, 0¹=0²/0¹ Which means 0¹=not defined.

[@nisargbhavsar25]

The exponent rule is only valid for non-zero real numbers.

[@peakpersona-yash]

@@nisargbhavsar25 thanks

[@alejandrodeharo9509]

too basic and boring, better make a video of the determinant of an anti diagonal matrix of nxn

[@colleen9493]

Is there anyone in the world who likes Cramer’s rule? Because I do not like it.

[@sugarfrosted2005]

I like it in theory just because of the "wait that works?" factor but beyond that it's computationally garbage.

[@criskity]

It's an easy concept, but it's computationally very inefficient.

[@jethalalgada379]

CNVideos so which is the best method to use? For easy calculation

[@kalkal8050]

@@jethalalgada379 Try Gaussian elimination.

[@jethalalgada379]

kal kal you mean the one using echelon form? Like creating 4*3 matrix and reducing it to zeroes etc

[@juanjael4465]

5th

[@helo3827]

I bet no one will respond to this

[@Apollorion]

You lost your bet, sorry pal.

[@Suraj-on7bf]

Hlo my name is Suraj and I am from India I want that u can prove the formula of arithmatic mean which is x=x1+x2+x3.......Xn/n

[@Suraj-on7bf]

Hlo my name is Suraj and I am from India I want that u can prove the formula of arithmatic mean which is x=x1+x2+x3.......Xn/n

[@Suraj-on7bf]

Hlo my name is Suraj and I am from India I want that u can prove the formula of arithmatic mean which is x=x1+x2+x3.......Xn/n

[@Suraj-on7bf]

Hlo my name is Suraj and I am from India I want that u can prove the formula of arithmatic mean which is x=x1+x2+x3.......Xn/n

[@Suraj-on7bf]

Hlo my name is Suraj and I am from India I want that u can prove the formula of arithmatic mean which is x=x1+x2+x3.......Xn/n