Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 1
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- Опубліковано 9 лют 2025
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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.
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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Wasted 42 years
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TRUE
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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!
I've already thanked you on another video, but I just can't thank you enough! My prof spent 1.5 hours on each matrix topic. None of it made sense and some people even got up to leave in the middle of lecture. Thank you for making everything 100% clear.
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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.*
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I’m watching this dude 9 years later and he saved me thanks
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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
13 years later and you're still helping people with this video ❤ thank you
man, having finished Diff Eq 2 years ago, i thought i would never hear Patrick's sweet soothing voice again. yet here i am for some review for solid modeling, and that voice is as beautiful as ever:')
6 years later and you're still saving lives. Thanks a tonne!
14 years later and he's still saving lives
@witsuz1 Wow my comment was 8yrs ago...
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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thanks! glad that i could help you after all this time :)
your videos still work like magic in 2024. I passed my calculus courses thanks to your videos 10-11 years ago.
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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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Best of luck!
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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.
Such a great video for learning.
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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
Thanks for your comment, u save my life
AHHHH I remember my teacher doing this method in the class but I forgot it. Thank you so much!! Hope I can use this is my exam tomorrow.
Thanks for making the video I understood it within 1 minutes and now I can solve every inverse questions in 3-5 minutes.
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In case someone is confused It's called "finding the inverse of A using the adjoint of A"
Where the adjoint of A = the transpose of the Cofactor matrix C ... adj = C^T
Holy mother of god, my brain is fried.
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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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This is the method for which I was looking for about an hour.
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A couple of hours before my exam, you actually saved my as*, And totally owned me teacher's metods. ( got 91% )!!!
much simpler and easier than school
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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.
Simple and. Precise
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Idk about everyone else but the diagonals helped me quite a bit
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It's so easy to goof up in Gauss elimination.
Thank you