Trimetime linear equation

Basic introduction

The three-dimensional linear equation group is a three-dimensional linear equation group that is zero zero. Three of X, Y, Z is in the real domain r. The standard form of the three-dimensional linear equation group consisting of equation is

Obviously, it is clear that X = Y = z = 0 is set, which is the zero solution of the equation group. When the coefficient line of the equation group is not zero, it only has the only zero solution. When the coefficient row D is zero, the equation group is in addition to the zone, there are countless non-zenque.

For example, equation

coefficient row D = 2 ≠ 0, the equation group has unique zero solution.

Any, equation group

coefficient row D = 0, and

Equations (1), (2) can be written into

to solve the

(T can take any real numbers).

Substant linear equations

System of Homogeneous Linear Equations refers to a linear equation group, a linear equation group

x ₁ = 0, x ₂ = 0, ..., x _{n < / sub> = 0 is obviously a solution, called zizici, other solving the two solutions (solving amount), and any number and arbitrary decision (solution) The product of the vector is still the solution of the homogeneous linear equation (demolith). The linear combination of any set of homogeneous linear equations is still the solution of the homogeneous linear equation (Sludge). Therefore, the general solution of the linear equation group constitutes a vector space called Qi Qi The solution space of the secondary equation group. Set AX = 0 is the n-line linear equation group of the M equation on the digital P, and the equation group AX = 0 is a full essential condition for non-zenix is ​​the rank R of the matrix A. A) The coefficient row is equal to zero.}