Homogeneous Linear System

Definition

Homogeneous linear system is defined as a linear system with $b_i=0$, for all $i=1,\dots ,n$.

It is written as

a_{11}x_{1} & + & a_{12}x_{2} & + & \dots & + & a_{1n}x_{n} & = & 0 \\ a_{21}x_{1} & + & a_{22}x_{2} & + & \dots & + & a_{2n}x_{n} & = & 0 \\ \vdots & & \vdots & && & \vdots & & \vdots \\ a_{m1}x_{1} & + & a_{m2}x_{2} & + & \dots & + & a_{mn}x_{n} & = & 0 \\ \end{matrix} $$ ## Related theorems - [[3 Reference/1.2 Gaussian Elimination#theorem-solution-of-homogeneous-linear-system|Theorem Solution of homogeneous linear system]] - [[3 Reference/1.2 Gaussian Elimination#theorem-121-free-variable-for-homogeneous-system|Theorem 1.2.1 Free variable for homogeneous system]] - [[3 Reference/1.2 Gaussian Elimination#theorem-122|Theorem 1.2.2]]