What is the homogeneous system in math?

In mathematics, a homogeneous system typically refers to a system of linear equations where all the constant terms are zero. This can be represented in the form (Ax = 0), where (A) is a matrix and (x) is a vector of variables. Such a system always has at least one solution, known as the trivial solution (where all variables are zero), and may also have non-trivial solutions if the matrix (A) does not have full rank. Homogeneous systems are fundamental in linear algebra and are often studied in relation to vector spaces and linear transformations.