Solving Systems Using Cramer's Rule

[@anonymous9217w2]

he knows a lot about all kinds of stuff , professor dave explains!

[@dannychenski687]

he knows a lot about the science stuff , professor dave explains!

[@ashrafhamdan7763]

Thank you, Professor Dave. Wonderful series and clearly explained. It's obvious that lots of effort went into preparing the material and making it so accessible. Amazing job!!

[@STKeTcH]

why are you the only one on youtube that can explain it so well?!

[@bikespike4150]

Professor dave, is as my friends and I would say: goated. Thank you for your hard work, it definitely does not go unappreciated.

[@dua7809]

Dear professor Dave, May Allah bless your soul and grant you all the good things you ever wished for. Thank you for saving us poor tortured engineers over the years. You're out superhero man

[@ConceptualCalculus]

I've been watching older Professor Dave vids. This is the first one I've seen with short hair. Looks good. And the vid is good, as usual.

[@krizh289]

what kind of monster watches math videos for leisure

[@artophile7777]

​@@krizh289 An average math enthusiast, such as me.

[@intisarhaq]

​@@krizh289 fr

[@jdanielcramer]

Wow.🤓so proud we have our own rule.🧐if only I could understand it🙃

[@nihalr385]

You use too many emojis

[@notveryrea1]

Lmfao

[@jdanielcramer]

@@nihalr385 🥹🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣😀😰🤢😻😙😬🥲🤡😼😝🙄👻😉🥳🥰😍😎😒🙁😩😔😋🥰😞🥺😤😡🤬🧐🥸🥸🥸🥸🥸🥸🥸🥸🥸

[@krizh289]

wow the Mr. Cramer Rule himself

[@Eduardo-tq5sk]

Kkkkkk,that's good!,and super!

[@Kasey-ww3oy]

Love your videos and I am a number one fan! You saved my life in math. Subscribed !

[@quevaex40]

Just watched this video and now I can clearly understand the rule.Thank you, Professor Dave.

[@skye-chor]

Such a simple yet effective explanation compared to all other videos. Many thanks

[@LwaziMgandela]

This video was so helpful. Thanks once again, Dave

[@acho8387]

Professor Dave never fails to explain!

[@duyvuonghoang5368]

thank you so much, the first recommended is you and now i can understand it

[@stranger5363]

Thank you sooooooo much for this video 🙏🙏🙏

Hi professor, can you also make a video on Rouche-Capelli theorem?

[@sameerrao1380]

Thanks a lot professor Dave !!

[@karpagalajju6888]

Thankyou so much I understood 💗🤌🏻

[@anugupta1596]

GOATED!!!!🐐

[@SaiTejaVaidya]

Thank you Professor .

[@mangasangames2645]

You rock, Professor Dave. Thanks 😂

[@andrewalday7834]

Thank you so much for your math videos!!! Keep them going!

[@starrynight5135]

Your videos are my life saverr🥲

[@timothymcglynn1935]

Thanks

[@isaiahlynch4113]

Can you do a video on the quadratic formula

[@ElonMozg]

i have no idea how the comprehension question answer was calculated, but the determinants of A2 and A3 are not -6 and -9, according to my own calculations, and multiple determinant calculators. Also, x=1 y=0 z=-1 works too

[@karansahani5110]

A3 will be 9 bro, not -9 And your calculations are wrong. You are saying that x=1, y=0, and z=-1. If you apply this in the equation the answer 7:01 will not.

[@div_yam2304]

Thank you so much!!!

[@aashirsstream9244]

thanks alot man this really helped

[@oddtistic_chris]

Thanks! This helped

[@moumenebmd2006]

thank youuu i love youuu halped me for the 1000 time

[@elenachen5146]

Thank you for the video! But what's the principle under this Cramer's rule?

[@WESLEYRUSSELSERENUELA]

How did you find A=12?

[@yigitcan824]

Its 6 right?

[@MuhammadHussain-vv9sq]

thank you amazing video

[@gianfrancobruschetta2423]

Hi, in the comprehension |A|=9 to me, i tries many times but i have always the same result, what am i doing wrong? Thanks.

[@sara-janepalisie255]

I also have 9

[@sara-janepalisie255]

Me 2

[@ssporthd9653]

@@sara-janepalisie255 It's 3....PEACE!

[@inhloco6969]

Thank you so much for the useful lesson!

[@miwan_d_mahmud]

Thanks 🥹🤍

[@ssporthd9653]

6:46 X=1 Y=-2 Z=3...PEACE!

[@presteenkagit1707]

can you o the same for 3x3 matrix using same variables

[@Salamanca-joro]

Lets gooooo i did 🎉🎉 i will get 100 in the final inshallah

[@eyouelsolomon3309]

Love the new hair

[@-miracle-]

Nice haircut 💇‍♂️

[@prajwalthorat28]

😅😅

[@aliahmed-qe4yh]

it was nice if you would have used x.y.... instead of x1 and x2.... any how very good explaination

[@realitygaming7302]

It took some mathematician 20 years to come up with and they expect high schoolers to learn it in a week

[@gana7206]

Next rule: if you square all the terms then take the determinant of each 3 by 3 matrix created by adding each column then invert those matrices you can find the transposition of one of the terms in the solution

[@pinklady7184]

Have you put this tutorial in any playlist?

[@ProfessorDaveExplains]

yep it's in the big math playlist as well as the linear algebra playlist

[@pinklady7184]

Professor Dave Explains Thank you very much. I will check out the playlist. Btw, I love your tutorials and thank you for making them.

[@pinklady7184]

Professor Dave Explains I have learned Crammer Rule. Yay! Thank you for the tutorials.

[@anonymous9217w2]

@@pinklady7184 why tf are you so excited, Imma gonna kick

[@artophile7777]

​@@anonymous9217w2 You need to be put back into your place it seems...

[@songul_t]

thank god this rule exists tbh

[@crocopie]

Short Hair Dave starts here. :D

[@japananh1]

His short hair looks awesome too.

[@pinklady7184]

Some woman probably had cut his hair while he was asleep. Imagine his reaction when he awoke. 😱

[@justinehercthehuman]

Confused with how this is easier for 10 equations with 10 variables when getting determinants is such a hassle for bigger matrices.

[@anuj_niser]

Hi Proff. Dave , You are looking like Indian actor RANBIR KAPOOR in your new look....... By the way , nicely explained

[@amruthagetta5971]

Thank you professor 😀☺️ your videos are right to the point and very easy to understand

[@Eduardo-tq5sk]

Thank you Doctor!

[@ozangeyik531]

Is not the determinant of A2 is 25?

[@kontiimanalatit8987]

To be honest gauss jordan is faster than cramer. Cramer is good for small systems. Very good explanation nonetheless

[@exytheboy5416]

I don't really get how those answers are appearing from 5:50

[@hana29971]

He took the determinant of the matrix A1, A2,A3

[@benr.7573]

A cool trick my professor taught is how to solve a system with fewer equations than variables - if you treat one of the variables as a constant and add it to the right-hand side, you can solve it in the same way and end up with two variables expressed in terms of the third.

[@kellyalltogether1747]

Thank you!

[@UnkownUnkown01]

Hey guys, I'm just wondering but, am I the only one who's watching this just because I actually want to learn math by myself and not because of school or any dumb test I have tomorrow? (Not even gonna mention how at school I'm not even learning this stuff yet lol)

[@tinkiniminki7712]

nice hair cut dude, love u

[@jenm1]

I think I prefer this to row operations. I’m not smart enough for the latter

[@aldanadagimpaulos7511]

5:47 i think the determinant is 20 not 12

[@mason.11]

Assuming you're referring to |A| as opposed to |A2| |A| = 2 det[3 -1, 2 2] - 1 det[0 -1, 1 2] +1 det[0 3, 1 2] (for clarity, I'm separating the rows of each matrix by a comma since I can't really type a matrix nicely on KZbin.) = 2(3*2 - negative1*2) - 1(0*2 - negative1*1) + 1(0*2 - 3*1) = 2(6+2) - 1(0+1) + 1(0-3) = 16 - 1 - 3 = 12

[@oj5554]

@@mason.11 why you wrote + not - in + 1(0*2 - 3*1)

[@vishnuprakashbharadwaj3211]

Hi Professor! How to find the consistency of system of linear equations with three variables?

[@krizh289]

A system is consistent if it has greater than or equal to 1 solution

[@antoniaangelopoulou4269]

really helpful

[@Attalla-t9b]

Seems like a question with a 4x4 matrix would take at least 10 minutes to solve if we're solving it using this method 😅 (and 10 minutes is quite fast)

[@nadachamseddine]

Thank you

[@ikramullah8892]

Plz upload more physics videos

[@starlords.7788]

I finally gfet it.

[@jussstdoiit]

the intro got me off guard

[@civic2980]

Id rather use cramers rule than reduce a matrix for every matrix i can. Reducing sucks.

[@blessingevahopkins3005]

You cut your hair😳😳

[@Eduardo-tq5sk]

What? Cramer's is " speed of light" I d do that instead!

[@kai.acadventure]

After watching you through 144 videos, BOOM... such a handsome haircut!

[@Jayanth-ci1ky]

❤❤❤❤

[@wesselbeer8041]

who is this? where is my dave?

[@adityaharsh4622]

A1 is wrong it should be 16

[@princeogomolaokibe2057]

X+Y=3 3X-Y=1 I couldn't get the right answer using cramer's

[@oomersheriff2998]

Haha seeing u with short hair caught me off guard lol

[@deraw.academy]

Chibaba ichi😅😅😅

[@artophile7777]

Cute ❤

[@fenrirunshackled4319]

Now, how does this prove the flat earth?

[@Earthy1671]

Did you have a hair cut?

[@ToanPham-wr7xe]

😮

[@bonniem1865]

GOD HE'S SO HOT WITH HIS HAIR SHORT

[@Poe561]

Shows how to solve the simple problem throws extra variables and another row with no explanation

[@hiwaadil6585]

Appreciate your videos but just to let you know that u have no difference than other teachers cuz u juat explain a bit and leave the hard examples for us to study

[@anirudhghatty]

Thanks