4.9 System of Homogeneous Linear Equations

4.9 System of Homogeneous Linear Equations

The system of following homogeneous linear equations:

is always satisfied by $x_1 = 0, x_2 = 0$ and $x_3 = 0$.

Therefore, the system (i) always has a solution $(0,0,0)$, which means that a system of homogeneous linear equations is always consistent.

The solution $(0,0,0)$ is called the trivial solution of the system (i).

A solution of the system (i) other than $(0,0,0)$ is called a non-trivial solution.