Thank you, sir! This was really helpful.😊

Thank you, you're a life saver 😂❤

A beautiful proof!

Very well explained sir, thank you so much😄

Hi there, great video very well done. I just wanted to note this only proves the cramers rule for a 3 dimensional case. However the proof does generalise to any dimension

What the fudge This is beautiful

wow it's a wonderful explanation! tnx a lot

Good Video. Thank you

thanks!

Thanks for the tutorial

Superb explanation!

Very clear explanation! Thank you 🙂

Excellent explanation great❤

Thank you so much!

Wow, that was super helpful!

Sir it's not R square but R2 please

It's amazing and elegant thank you 😊

Thx for this amazing explanation! You're a lifesaver :)

okay

This is a super helpful video. Can't believe it's got only, like, 3,000 views.

This is the most beautiful and elegant proof I've ever seen. I can't believe something that seemed so random at first suddenly becomes clear and obvious

what if i use x1 to times the second column and mess up the whole order?is it still provable?

thank you very much!!! excellent proof!!!

Nice video!

That’s amazing …

You sir, are a legend! Thank you!

Great explanation....

Cool proof!

this is awesome explanation!

Really well explained and a great result! Thank you for sharing

Thanks

Thank you

Very nice proof, Thanks.

The graphs look like an eyeball. Interesting!

Don't worry man. My Multivariate Calculus professor said I gave him a severe headache. During the midterm exam, I got every question right and even got the extra credit one. Can you imagine the look on the Japanese Exchange Students when they seen me do that? I didn't know they'd take it to heart. I just wanted to do my best.

You do know that you can do the same thing if you start at the bottom and it's easier because of the zero component which is in the 3rd row, 2nd Column which multiplies by that cofactor and makes it go to zero. That way only have the coefficients and cofactors in the 3rd row first column, and the 3rd row 3rd column. Try it. It's a lot faster.

I remember when I took Multivariate Calculus at Purdue University. That was an extra question on one of his easier tests. It's a headache, but I whizzed through it back then. I was in my 20's and full of vinegar. Kramer's Rules is awesome. Have you ever tried to derive Kramer's Rule using the Kronecker Delta Method? That is, a generalized formula? I did that when I took Linear Algebra. It was fun. Of course the other students hated me because I was always the brains in the classes, but I acted like it was easy. Being honest, Multivariate Calculus was the most difficult mathematics course I took there. I earned a B, but that's only because the guy teaching it was a nut and claimed that he didn't grant A's. I had the curve in the class. I got an A in advanced Linear Algebra, Tensor Analysis, and Differential Equations. It was funny because I never studied but crammed at the last minute. I also held down a full time job. ha ha. People wanted to kill me for that!

It should be pi/4 at 27:13