Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 1
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- เผยแพร่เมื่อ 28 ส.ค. 2024
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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.
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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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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.
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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
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instead of saying reflection about diagonal, appropriate to say taking Transpose
sayak chowdhury
Unnecessary nit picking. Reflection more meaningful for most.
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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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.
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This is the method for which I was looking for about an hour.
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