1, diagonal method: The standard method is to add the first column and the second column of a given determinant to the right. We call the diagonal of determinant from the upper left corner to the lower right corner as the main diagonal, and the diagonal from the upper right corner to the lower left corner as the secondary diagonal. At this time, the value of the third-order determinant is equal to the difference between the product of three numbers on the main diagonal and the product of three numbers on the diagonal parallel to the main diagonal minus the product of three numbers on the diagonal parallel to the sub-diagonal.

2. Algebraic cofactor: cofactor of an element of a determinant: the determinant cuts off the elements in the row and column where the element is located, and arranges the remaining elements as they are, thus obtaining a new determinant. Algebraic cofactor of determinant element: the product of cofactor of determinant element and its corresponding sign. That is, the determinant can be expanded into the sum of the products of elements and their corresponding algebraic cofactors by rows or columns.

Extended data:

Through analytic geometry, linear algebra can be expressed concretely. The theory of linear algebra has been extended to operator theory. Because the nonlinear model in scientific research can usually be approximated as a linear model, linear algebra is widely used in natural science and social science.

The research objects of linear algebra are vectors, vector spaces, linear transformations and finite dimensional linear equations. Vector space is an important subject in modern mathematics. Therefore, linear algebra is widely used in abstract algebra and functional analysis;

With the in-depth study of linear equations and linear transformation of variables, determinant and matrix came into being in the period of 18 ~ 19 century, which provided powerful tools for dealing with linear problems and promoted the development of linear algebra. The introduction of the concept of vector forms the concept of vector space. All linear problems can be discussed from the viewpoint of vector space. Therefore, vector space and its linear transformation, as well as the related matrix theory, constitute the central content of linear algebra.