The second question:

The third question:

The fourth question:

The fifth question:

This part of the extended material mainly examines the knowledge points of linear algebra:

A branch of linear algebraic mathematics, whose research objects are vectors, vector spaces (or linear spaces), linear transformations and linear equations with finite dimensions. Vector space is an important subject in modern mathematics. Therefore, linear algebra is widely used in abstract algebra and functional analysis; 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.

Linear relationship means that the relationship between mathematical objects is expressed in linear form. For example, in analytic geometry, the equation of a straight line on the plane is a binary linear equation; 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.