Is "n" here the order of the matrix? If so then, by a row reduction to diagonal or triangular form, you can show that the last row becomes all "0"s.encomes said:How can I get the determinant of this matrix?
1-n 1 ...1 1
1 1-n ...1 1
. . . .
. . . .
1 1 ... 1 1-n
I think that the answer is 0 but... why?
Thank you.
The determinant of a matrix is a scalar value that is computed from the elements of the matrix. It is a measure of the matrix's size and how the matrix affects the linear transformation it represents.
The determinant of a matrix can be calculated using various methods, such as cofactor expansion, Gaussian elimination, or using properties of determinants. The method used depends on the size and structure of the matrix.
The determinant of a matrix has several important applications in mathematics and science. It is used to solve systems of linear equations, determine invertibility of a matrix, compute volumes of parallelepipeds, and more.
The determinant of a matrix has various properties, such as linearity, multiplicativity, and the fact that it changes sign when rows or columns are interchanged. These properties are useful in simplifying calculations and proving theorems involving determinants.
The determinant of a matrix is closely related to the eigenvalues and eigenvectors of the matrix. In fact, the determinant of a matrix is equal to the product of its eigenvalues. This relationship is useful in finding eigenvalues and eigenvectors, as well as understanding the behavior of a matrix's transformation.