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matrix formula proofs

Anonymous Sat 31 Jul 00:19:00 2021 No.13454304 View Reply Original Report

Quoted By: >>13454369 >>13454722 >>13455352 >>13456258 >>13457150

Are there intuitive proofs for the determinant of a 3x3 matrix formula (preferably geometric)

and for the adjunct of matrices (cofactors minors and sign rule

Anonymous

Anonymous Sat 31 Jul 2021 00:55:00 No.13454369 Report

Quoted By: >>13454396

>>13454304
>intuitive proofs
That's subjective so a you problem

Anonymous

Anonymous Sat 31 Jul 2021 01:14:03 No.13454396 Report

Quoted By:

>>13454369
just geometric for the 3x3 matrix

Anonymous

Anonymous Sat 31 Jul 2021 03:48:31 No.13454722 Report

Quoted By:

>>13454304
Yes. Using Clifford algebra you can visualize this as a the volume element of a oriented set of multivectors.

Anonymous

Anonymous Sat 31 Jul 2021 08:57:06 No.13455352 Report

Quoted By:

>>13454304
yes. you can define determinant axiomatically as the oriented volume of a parallelepiped spanned by a set of 3 vectors (columns of the matrix). you write the down the properties that should hold and then use them to derive the exact formula involving permutations, it simply pops out.
the formula for adjunct matrix follows from the Laplace expansion for the determinant, and the Laplace expansion is basically the relationship between the oriented volume of a solid and the areas of its projections onto the yz, zx, and xy planes. it can be derived using exterior algebra.

Anonymous

Anonymous Sat 31 Jul 2021 17:31:24 No.13456258 Report

Quoted By: >>13456292 >>13457250

>>13454304
There is nothing intuitive about determinants.

Anonymous

Anonymous Sat 31 Jul 2021 17:46:48 No.13456292 Report

Quoted By:

>>13456258
>t. doesn't understand determinants

Anonymous

Anonymous Sat 31 Jul 2021 22:00:53 No.13457150 Report

Quoted By:

>>13454304
Read this:

http://www.math.unt.edu/~tushar/project%20ideas/monthly%2096%20hannah%20geometric%20determinant.pdf

Anonymous

Anonymous Sat 31 Jul 2021 22:30:18 No.13457250 Report

Quoted By:

>>13456258
yes there is the education system has failed you

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