What Is a Determinant?

In mathematics, a determinant is a function whose domain is det's matrix A, which takes a scalar value and is written as det (A) or | A | Whether in linear algebra, polynomial theory, or in calculus (for example, in the integral integration method), determinants have important applications as basic mathematical tools.

n-order determinant

Assume

A row (or column) in determinant A is multiplied by the same number k, and the result is equal to kA.

The determinant A is equal to its transposed determinant AT (the i-th row of AT is the i-th column of A).

If a certain row (or column) in the determinant of the n order | ij |; , ..., bn; the other is 1, 2,, n; the elements on the other rows (or columns) are exactly the same as | ij |.

The two rows (or columns) in determinant A are interchanged, and the result is equal to -A. Multiply each element in a row (or column) of determinant A by one and add it to the corresponding element in another row (or column). The result is still A. ^[1]