Science:Math Exam Resources/Courses/MATH152/April 2022/Question A12/Hint 2

Consider the associated homogeneous equation $A$:

$$Ax=0.$$

What can you say about the solutions here?

Unless $b$ is the $0$ vector, solutions of the homogenous equation are not solutions of the original equation. However, given a solution of the original equation, can you use knowledge about the space of homogenous solutions to say something about the full set of solutions?