Solving a 4x4 Determinant for Math Projects

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Discussion Overview

The discussion revolves around methods for solving a 4x4 determinant, focusing on various mathematical techniques and approaches. Participants explore theoretical and practical aspects of determinant calculation, including Gaussian elimination and expansion by minors.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about methods for solving a 4x4 determinant.
  • Another suggests converting the matrix to upper triangular form using Gaussian elimination, proposing that the determinant is the product of the diagonal elements, although this is presented with some uncertainty.
  • Some participants advocate for expanding by minors as a method, providing links to resources for further reading.
  • One participant mentions that applying the permutation definition results in 24 terms to sum, indicating a preference for the minors method due to its perceived simplicity.
  • A detailed explanation of the general definition of an n by n determinant is provided, emphasizing the role of permutations and the sign associated with them, while also reiterating the row reduction and minors methods as simpler approaches.

Areas of Agreement / Disagreement

Participants present multiple methods for calculating the determinant, including Gaussian elimination and expansion by minors, but there is no consensus on which method is superior or preferred.

Contextual Notes

Some methods mentioned may depend on specific assumptions about the matrix or the context in which the determinant is being calculated. The discussion does not resolve the complexities involved in each method.

Who May Find This Useful

Students and educators involved in mathematics projects, particularly those focusing on linear algebra and determinants.

jebeagles
I was doing a math project, and I was wondering if anyone knew how to solve a 4x4 determinant.
 
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Convert it to it's upper triangular form using Gaussian Elimination and the determinant should be the product of it's diagonal elements. I think.
 
Aplying the permutation definition, you will have 24 terms to sum. Its much easier to do by minors.
 
The DEFINITION of a genereal n by n determinant is this: form all possible products taking one number from each row and column. There will be n! ways to do this. If you write the terms so that the numbers are in order of the columns, the row numbers will be a permutation of 1,2,3...n. Multiply each product by -1 if this is an odd permutation, 1 if even permutation, and add.

The simplest way to calculate it is row reduce as Jhageb suggested.

Second simplest way is to "expand by minors".
 

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