The equation of spatial plane is a ternary linear equation, and the spatial straight line is regarded as the intersection of two planes, which is represented by an equation group composed of two ternary linear equations. A linear equation with n unknowns is called a linear equation. A function whose variables are linear is called a linear function. Linear relation problem is called linear problem for short. The problem of solving linear equations is the simplest linear problem.
2. As an independent branch discipline, linear algebra has a long history, although it was only formed in the 20th century. The problem of "chicken and rabbit in the same cage" is actually a simple problem of solving linear equations.
The oldest linear problem is the solution of linear equations, which has been completely described in the ancient Chinese mathematical work "Nine Chapters Arithmetic Equations", and the method in it is essentially equivalent to the elementary transformation of rows of the augmented matrix of modern equations and the method of eliminating unknowns.
3. Every linear space has a basis.
4. One? n？ Okay？ n？ Non-zero matrix of column? A, if there is a matrix? b？ Manufacturing? AB？ =? Ba? =E(E is identity matrix), then? Answer? Is nonsingular matrix (or invertible matrix), and b is the inverse matrix of a.
5. The matrix is nonsingular (invertible) if and only if its determinant is not zero.
6. A matrix is nonsingular if and only if the linear transformation it represents is automorphism.
7. A matrix is semi-positive definite if and only if each of its eigenvalues is greater than or equal to zero.
8. A matrix is positive if and only if each of its eigenvalues is greater than zero.
9. Cramer's rule for solving linear equations.
10, and judge the relationship between augmented matrix and coefficient matrix of non-zero real root linear equations.