Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 1
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- Опубліковано 1 сер 2010
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Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 1. Besides using row reduction, this is another way to find the inverse of a 3 x 3 matrix.
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For those who want a simpler method for 5:10 and on (without "reflecting things about the diagonal"): Just *transpose* the matrix, which means the first row becomes the first column. The second row become the second column. The third row becomes the third column. The nth row becomes the nth column. It's easier to remember this way.
Thanks
Thank you.
That is adjoint, right?
@@dremr2038 Yes, finding the cofactor of each element of the matrix and transposing it, gives us the adjoint of the matrix in question. Dividing that by the determinant of the original matrix gives us the inverse of the matrix.
Ok
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I've watched quite a few videos on finding the inverse of a 3 x 3 matrix and so far your method seems like the easiest way to do it without making mistakes. Thanks for sharing!
Why do these formulas work, who came up with this method for finding the inverse of a 3x3 matrix and what was going through his head at the time?
I Know what you mean like gezz.. some guy comes up with a method then others find a better way to do what you came up with... like WTF... its so Heavy..
Mthabisi Bokete with linear algebra in general i see a lot of fancy tricks and algorithms for solving problems but never a proof showing why they work
Marcus Fenix Aliens.
Marcus Fenix You don't want to see the proofs lol. Well, some are easy and some are harder, some are very trivial, but extraordinarily long. Determinants revolves a lot around matrix multiplication. Matrix multiplication's proof isn't too bad if you remember your matrix as a set of vectors in the defined r-space.
derekroolz I saw some wikepedia proof for the cofactor expansion and didn't understand it at all
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Good work Patrick. Identifying the matrix of minors, matrix of cofactors and the adjoint matrix will help viewers follow and understand the various steps in arriving at the inverse matrix of the original 3 by 3 matrix.
You always find the best way to explain things Teacher! thank you alot..
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Glad you like my videos!
I did indeed! I finally used it today and aced it! xD Thanks so much again for taking the time to help others! (:
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this was thorough and very well explained.
thank you so much for the help
You confused me with the whole diagonalization thing. Took me a second to realize it's just a transpose lol...
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I thank him since now I know how to transpose a 3 by 3 matrix conveniently
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5:25, It can also be referred to finding the transpose or adjoint of the matrix. The rows become columns, and the columns become the rows. Good job.
Yeah this is the trick !
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What my teacher says :
"It's simple :" *Complicated, incomprehensible stuff on the board wich he erases every seconds*
Him :
*Explains ORALLY an actual simple method in addition of explicitly witting it down AND doing it on UA-cam, giving us the ability to pause or rewind.*
Why can't teachers be this straight forward?
Thank you so much for the videos! I was running late on recapping and this video (hopefully) made the difference.
Thanks for making the video I understood it within 1 minutes and now I can solve every inverse questions in 3-5 minutes.
This is the method for which I was looking for about an hour.
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Thank you so much. It really helped me alot
I have a midterm tomorrow, thanks a ton brother!
I'm hopefully gonna ace it tomorrow thanks to you!
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Holy mother of god, my brain is fried.
My brain exploded
In my opinion, the only difficult part of this tedious process is avoiding making small mistakes. The concept itself is fairly easy to grasp.
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Super good video, clear and easy to understand!!
Really easy to understand! Thank you so much!!!
awesome sir.very interesting,thanks for teaching the 3*3 matrix very easily
this is so much better than reading the book and reading the examples which doesn't make much sense most of the time... thank you for making it easy.
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@no2475 unfortunately, that is how many math classes are structured in usa. when i taught, we had to go fast as we had to cover waaaaaaay to much stuff typically; if we fell behind, we got in trouble at the end of the year. no good for anyone.
thank u very much i didn`t understand sign when doing cofactors but now i do u the best
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Thank you. Watching this 1 hour before my exam, learned something new
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finding an inverse is a truly painful process, but u did it in a way that made me understand it.
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Easy, quick. Thanks
you just explained this way better than my prof and TA could. Thank you
Wow. Thank you so much. I actually prefer this method over Gauss Jordan for inverses because Gauss Jordan for me is tideous and mistakes are easily made so with this one, it is easy to keep track of your workings.
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Trust me I found it hard to find a strategy for finding co factors ..... And u jxt made it look so easy thank u
thank u so much it was so helpful and easy to understand ( i study in frensh and am not very good in english ) good Luck 😊
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Thank you very much. Very clear guide.
Way sampler than gauss elimination. Why doesn't my math teacher teach this.
Actually for simpler matrix entries, I think the Gauß elimination is much faster... Sometimes you can find the inverses with a handful of steps... This seems to be for tougher matrices... It's good to know both I guess.
Gaussian elimination has fewer steps to find the inverse. The determinant is computationally inefficient
Gaussian works for any order of the matrix.
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Thank you so much I just got understand how to do it
You made it very easy, thank you