Wow, sir... with that 'real life' example, you just made the concept of the inverse of a product so ridiculously simple. Thank you for thinking that out and using such an easy to grasp example.
another great vid! that last comment foreshadowd a deep insight 😄 I paused the video before you gave the answer and came up with: AB(AB)-1 = 1 ; Α-1AB(AB)-1 = A-1 : B(AB)-1 = A-1 ; B-1B(AB)-1 = B-1A-1 ; (AB)-1 = B-1A-1
Another example from life is putting on your socks, then your shoes. If you want to do the reverse you start by taking off the shoes, then your socks. There are countless examples. And if you look at Matrix Multiplication as chaining linear transformations together (like in 3Blue1Brown's Series "The Essence of Linear Algebra") it also makes complete sense.
Professor, it was really nice explanation. I have one question. You defined A and B as two distinct action and related B^-1 and A^-1 with (AB)^-1. But the inverse of the whole AB product is not demonstrated! You will go back side and take right while taking the inverse of AB. Still your analogy will work, but the left side of the equation will be something different from what you demonstrated! You might opine on that. Thank you.
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Wow, sir... with that 'real life' example, you just made the concept of the inverse of a product so ridiculously simple. Thank you for thinking that out and using such an easy to grasp example.
another great vid! that last comment foreshadowd a deep insight 😄
I paused the video before you gave the answer and came up with: AB(AB)-1 = 1 ; Α-1AB(AB)-1 = A-1 : B(AB)-1 = A-1 ; B-1B(AB)-1 = B-1A-1 ; (AB)-1 = B-1A-1
Thanks for making the concept so easy to understand!
Beautiful indeed
You made this so simple and intuitive. Thanks, very helpful, and very well done.
Glad it was helpful!
Nice example from life, math is so related to the physical entities of life but people don't get it.
Excellent expression.... Thank you very much
Your video is very helpful. Thanks
Another example from life is putting on your socks, then your shoes. If you want to do the reverse you start by taking off the shoes, then your socks. There are countless examples. And if you look at Matrix Multiplication as chaining linear transformations together (like in 3Blue1Brown's Series "The Essence of Linear Algebra") it also makes complete sense.
That is a great example!
@@MathTheBeautiful Thank you for the amazing series. I just finished this playlist and learned a lot.
Great video thanks very much
Thank you , now it is very simple 👍🏻
Thank you - I love your sentiment!
AT 3:00 timestamp, I literally was laughing on myself since I was not able to get the crux of matrix inversion up until now.
Professor, it was really nice explanation. I have one question. You defined A and B as two distinct action and related B^-1 and A^-1 with (AB)^-1. But the inverse of the whole AB product is not demonstrated! You will go back side and take right while taking the inverse of AB. Still your analogy will work, but the left side of the equation will be something different from what you demonstrated! You might opine on that. Thank you.
where can I find the proof videos?
I had big plans for a proofs playlist, but so far it has only three videos: czcams.com/video/f7M-kOjMl6k/video.html&ab_channel=MathTheBeautiful
sir what happens when we multiply two same inverse matrix like M-1 × M-1 ?
You get the inverse of M²
How would you find the inverse of the product of three or four or n matrices ?
i.e you find (AB)^-1 = B^-1A^-1 but what about (ABC)^-1 or (ABCD)^-1?
(ABC)⁻¹ = (BC)⁻¹ A⁻¹ = C⁻¹⁻B⁻¹ A⁻¹ = C⁻¹B⁻¹A⁻¹
@@MathTheBeautiful thanks. it is helpful now.
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