How Do You Calculate the Determinant of a Matrix in Linear Algebra?

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Discussion Overview

The discussion revolves around calculating the determinant of a matrix in linear algebra. Participants explore different approaches and considerations related to the determinant, including the application of row and column operations.

Discussion Character

  • Homework-related, Technical explanation, Debate/contested

Main Points Raised

  • Some participants propose that the determinant could be -30, referencing an external article for support.
  • One participant notes that the linked document discusses the applicability of row operations to column operations, emphasizing that the determinant of the transpose is equal to the determinant.
  • A participant expresses confusion regarding the application of the Jacobi theorem, specifically questioning how a certain value was derived in the context of the determinant calculation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the determinant's value, and there are competing views regarding the application of theorems and operations related to determinants.

Contextual Notes

There are limitations regarding the assumptions made about theorems and operations, particularly concerning the applicability of the Jacobi theorem and the handling of row versus column operations.

Who May Find This Useful

Students and individuals interested in linear algebra, particularly those seeking clarification on determinant calculations and related theorems.

Chipset3600
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Hello guys, can someone help me with this question please?

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pickslides said:
The answer could be -30.

This article may be helpful

http://science.kennesaw.edu/~plaval/math3260/det2.pdf

What the linked document says about row operations also applies to column operations as the determinant of the transpose is equal to the determinant. It is both row and coumn operations that are needed here (or switching between the matrix and its transpose, which is the same thing).

CB
 
pickslides and CaptainBlack, the problem was that i throug the theorem of Jacobi was only for rows, than i was thinking how he got the "5" in second column. thank you guys!
 

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