Linear Algebra

For a homogeneous linear system $A x = 0$ where $A$ is an $m \times n$ matrix with $\text{rank}(A) = r < n$, which statements are TRUE?

Options:

• (A) The system always has the trivial solution $x = 0$
• (B) The system possesses infinitely many non-trivial solutions
• (C) The nullity (dimension of solution space) is $n - r$
• (D) The system has no solutions whatsoever