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

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To calculate the determinant of a matrix, both row and column operations can be utilized, as the determinant of a matrix is equal to that of its transpose. The discussion highlights a potential answer of -30 for a specific matrix determinant. A linked article provides additional insights into the calculation process, particularly regarding row operations. Clarification was made regarding the application of the Jacobi theorem, which initially focused only on rows. Understanding these concepts is essential for accurately determining the determinant in linear algebra.
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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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