Only when the elements of two determinants differ by one row (or one column) can they be added directly (the same row (column) is unchanged, and the elements of different rows (columns) are added separately). Determinants with the same number of rows and columns can be added or subtracted; Secondly, addition and subtraction are the elements in the corresponding rows and columns in the previous determinant minus the elements in the corresponding rows and columns in the latter determinant.
In mathematics, determinant is a function of matrix A whose domain is det, and its value is scalar, which is denoted as det(A) or |A|. Its characteristics can be summarized as multilinear form, which makes determinant a function describing "volume" in Euclidean space.
The difference between matrix and determinant: a number multiplied by a matrix means that this number is multiplied by each element of the matrix; Multiplying a determinant by a number can only be used to multiply a row or a column of the determinant, and raising the common factor can also be used. After elementary transformation, the rank of the matrix remains unchanged; The determinant may change its value after elementary transformation. Wait a minute.
In mathematics, determinant is a function of matrix A whose domain is det, and its value is scalar, which is denoted as det(A) or |A|. Whether in linear algebra, polynomial theory or calculus (such as substitution integral method), determinant, as a basic mathematical tool, has important applications.
nature
1, 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 row (or a column) in the n-order determinant |αij|; The determinant |αij| is the sum of two determinants, and the I-th row (or column) of these two determinants.
2. Two rows (or two columns) in determinant A are interchanged, and the result is equal to-A. Multiply each element in one row (or one column) of determinant A by a number, and then add it to each corresponding element in another row (or another column), and the result is still A.