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

[Chipset3600]

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

View attachment 335

 

[pickslides]

The answer could be -30.

This article may be helpful

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

 

[CaptainBlack]

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

 

[Chipset3600]

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!

 

[blue_raver22]

Sure, I can help you with your question about determinants in linear algebra. A determinant is a mathematical value that can be calculated for a square matrix. It represents the scaling factor of the matrix, and is used in various applications such as solving systems of linear equations, calculating areas and volumes, and finding the inverse of a matrix.

To calculate the determinant of a matrix, you can use various methods such as the cofactor expansion or Gaussian elimination. The determinant of a 2x2 matrix can be found by multiplying the elements along the main diagonal and subtracting the product of the elements along the other diagonal. For larger matrices, the calculation can be more complex.

Determinants have many important properties, such as being equal to zero if the matrix is singular (meaning it has no inverse), and being equal to the product of the eigenvalues if the matrix is diagonalizable. They are also useful in solving systems of linear equations, as the determinant can determine whether the system has a unique solution, no solution, or infinitely many solutions.

I hope this helps to answer your question about determinants in linear algebra. Let me know if you have any further questions or need clarification on anything.