1. Solving linear equations: Determinants can be used to solve linear equations, such as Cramer's law. Cramer's rule is a method in linear algebra, which is used to solve linear equations. It represents the coefficient matrix and constant term vector as a determinant, and then solves the solution of linear equations through a series of operations on the determinant.
2. Calculate the inverse matrix of a matrix: Determinants can be used to calculate the inverse matrix of a matrix. If the determinant of a matrix is not zero, then the matrix has an inverse matrix. Inverse matrix has applications in many fields, such as computer graphics, physics and engineering.
3. Determine whether a matrix is reversible: Determinants can be used to determine whether a matrix is reversible. If the determinant of a matrix is zero, then the matrix is irreversible.
4. Calculate eigenvalues and eigenvectors of matrices: Determinants can be used to calculate eigenvalues and eigenvectors of matrices. Eigenvalues and eigenvectors have applications in many fields, such as physics, chemistry and biology.
5. Solving geometric problems: Determinants can be used to solve some geometric problems, such as solving parallelogram area, triangle area and volume.
In a word, determinant in higher mathematics has a wide range of applications in life. It can not only help us solve various practical problems, but also promote the development of science and technology.