structural:reformatting, information:highlighting
Homogeneous solution set

Every homogeneous system has at least one solution, known as the zero (or trivial) solution, which is obtained by assigning the value of zero to each of the variables. If the system has a non-singular matrix (det(A) ≠ 0) then it is also the only solution. If the system has a singular matrix then there is a solution set with an infinite number of solutions. This solution set has the following additional properties:

These are exactly the properties required for the solution set to be a linear subspace of R. In particular, the solution set to a homogeneous system is the same as the null space of the corresponding matrix A.