Generally speaking, it is only said that there is only zero solution, which is linearly irrelevant, while AX=0 is linearly related when there is a non-zero solution. Similarly, if AX=b has a solution, that is, b can be expressed linearly by a, and if there is no solution, that is, b cannot be expressed linearly by a.

No solution: linear algebra has no solution, that is, no answer can satisfy the meaning of the problem.

There are infinite solutions: linear algebra has infinite solutions, that is, there are countless answers that can satisfy the meaning of the problem.

concept

Linear algebra is a branch of algebra, which mainly deals with linear relations. 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. Functions whose variables are linear are called linear functions. Linear relation problem is called linear problem for short. The problem of solving linear equations is the simplest linear problem.