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- Опубликовано: 18 сен 2024
- Checking for which a, b, c, d the system ax + by = e and cx + dy = f always has a unique solution without using determinants.
This video is called Abby because I originally typed in ax+by on my phone and it autocorrected to abby, haha
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ABBY!!!!!!!!!!!!!!!!!
It would have been interesting to note the geometric interpretation of this problem. A unique solution exists if ad-bc is not equal to zero, i.e., -a/b is not equal to -c/d. Those are the slopes of the two lines!
Edit: -a/b, the slope of the first line
Oh wow, you’re right!!! Never realized that! 😮
And something similar would be true for planes in terms of normal vectors!
@@drpeyam Exactly!
Hey, Dr. Peyam. I would like to share a suggestion. Would you consider making a video on the infamous question number 6 from the 1988 Australian Math Olympiad: Let a and b be positive integers such that ab+1 divides a^2+b^2. Show that
; a^2+b^2/ab+1 is the square of an integer.
Being such a ridiculous question at its time and being completely solved only by one man, who was a point less for a gold medal (got silver only), I find this question to be really obscure and I think it will be interesting to see you showing a solution on it in a video.
These are both equations that are lines. There are three possible solutions. They intesect at a single point OR the intesect at every point (they are the same line) or they are parallel and never intesect. Simple solutions easily shown by geometic drawings. And lastly we are assuming that this is euclidean geometry.
come together linear algebra - abby road!
In Z: a diophantine linear equation ax+by = e has a solution iff gcd(a,b) divides e. We can apply that to the second equation as well, finding a,b,c,d and then, in the end we will compute e and f.
Yes. Thank you Mr. Peyam! Very interesting this aspect! You cannot have rows or columns completely filled with zeros without consequences!
can anyone explain the parentheses? the < > part... why do pivots limit amount of solutions?
Abie (seedy he-effigy), hate-shy Jake, a lemon? Oh, pique! You arrest tea, you video bull, you ex-wise head!
Jack Sainthill I wonder if anyone else got this
@@fluxtwee2804
Most people have no idea what they're missing. ;)
Cheers - and well done. :)
BTW: Camera angle is perfect ion this video, as it allows us to follow your writing as opposed to when the camera faces the whiteboard (in that case, you are in front of what you're writing).
I love your show, by the way.
Thank you!!! bprp suggested that camera angle, I’ll make my videos like that from now on!
@@drpeyam i like this aswell, but i think the angle may be a little bit too steep?
The angle works well as it appears as if you're left handed.
Easiest problem ever. Literally.
This is ec af
WOW! that's the formula for the determinant
And when we dont have a non solution? in this case: a/c = b/d diferent to e/f ?
Hey Doc., quick suggestion: try to make shorter videos, like this one.
20+ min videos keep viewers away, I think ;)
Yep, I’m gearing towards that as well :) And they’re so much easier to make
well they are two lines so as long a/b != c/d it should be a unique solution, atbleastbin the real numbers.. now lets watch the video and see howbwrong i am lol
Grüße aus Österreich!
7:42 blooper?
Gianpaolo Di Nino ?
Can't read from the board Dr Peyam.
I know
Hey Dr.peyam!! :D :D
Hi!!! 😄
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