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ahmednet24
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how we can find the determinant of non square matrix ??
ahmednet24 said:in fact I try to understand the paper that I mention to it,I don't know how they find the determinant of a matrix of size 2x3
A determinant is a mathematical value that can be calculated for a square matrix, which is a matrix with an equal number of rows and columns. However, it is also possible to calculate the determinant of a non square matrix, which is a matrix with a different number of rows and columns. The determinant of a non square matrix is used to determine the consistency and uniqueness of a system of linear equations.
The determinant of a non square matrix can be calculated by first creating a square matrix from the non square matrix by adding rows or columns of zeros. Then, the determinant can be calculated using the same methods as a square matrix, such as Gaussian elimination or Cramer's rule.
The determinant of a non square matrix represents the signed volume of the parallelepiped spanned by the columns or rows of the matrix. In other words, it represents the scaling factor of the transformation described by the matrix.
The determinant of a non square matrix is important because it is used to determine the consistency and uniqueness of a system of linear equations. It can also be used to calculate the inverse of a non square matrix, which is useful in solving systems of equations and in various applications in physics and engineering.
Yes, the determinant of a non square matrix can be negative. The sign of the determinant depends on the number of row and column swaps required to put the matrix into its reduced row echelon form. If an odd number of swaps is required, the determinant will be negative, and if an even number of swaps is required, the determinant will be positive.