Answer: If the columns of A are linearly independent, the only way to have Ax=0 is that x = 0. If the columns of A are linearly dependent, you may have Ax = 0 also for x ≠ 0.
Step-by-step explanation:
The equation Ax = 0 is a homogeneous equation. A homogeneous equation is always consistent and has a trivial solution if and only if the equation has at least one free variable. The solution x = 0 is called the trivial solution. If the columns of A are linearly independent, the only way to have Ax=0 is that x = 0. If the columns of A are linearly dependent, you may have Ax = 0 also for x ≠ 0.
