Fix a matrix a and a vector b. suppose that y is any solution of the homogeneous system ax=0 and that z is any solution of the system ax=b. show that y+z is also a solution of the system ax=b.

Step-by-step explanation:

Let be a solution vector of the homogeneous linear system , then, .

On the other hand, suppose that is a solution vector of the non-homogeneous linear system , that is, .

Now, considering the previous assumptions, you have:

The above demonstrates that the vector satisfies the system . Then is a solution of the non-homogeneous linear system

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