If Ax=0Ax = 0Ax=0 is a homogeneous system with 333 variables and rank(A)=3\text{rank}(A) = 3rank(A)=3, what is the solution xxx?
Infinitely many solutions.
Only the trivial solution x=(000)x = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix}x=000.
The system has no solutions.
The solution depends on one free parameter.