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

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SUMMARY

The discussion focuses on calculating the determinant of a matrix in linear algebra, specifically addressing the use of row and column operations. Participants reference the determinant of the transpose being equal to the determinant itself. A key point includes the application of Jacobi's theorem, which is initially misunderstood as only applicable to rows. The correct approach involves both row and column operations to accurately compute the determinant.

PREREQUISITES
  • Understanding of linear algebra concepts, particularly determinants
  • Familiarity with row and column operations on matrices
  • Knowledge of matrix transposition and its properties
  • Basic grasp of Jacobi's theorem in linear algebra
NEXT STEPS
  • Study the properties of determinants, including the effect of row and column operations
  • Learn about matrix transposition and its implications on determinants
  • Explore Jacobi's theorem and its applications in determinant calculations
  • Practice calculating determinants using various methods, including cofactor expansion
USEFUL FOR

Students and educators in mathematics, particularly those studying linear algebra, as well as anyone seeking to deepen their understanding of matrix determinants 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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