There are at least two answers to this question; one of these is more educative and the other one is at least as educative (in a different and profound way) as well as practical. Method 1 The first method is a more introductory level method. It is helpful to know it and good to read it as a refresher even if one is more advanced student of the topic. A linear system $\mathbf{Ax=b}$ is homogeneous when $\mathbf b=\mathbf 0$ and nonhomogeneous…