Suppose that x1=-1, x2=2, x3=4, x4=-3 is a solution of a non-homogeneous linear system ax = b and that the solution set of the homogeneous system ax=0 is given by the formulas: x1= -3r +4s, x2=r-s, x3=r, x3=sa) find the vector form of the general solution of ax=bb) find the vector form of the general solution ax=0

The answers will be as simple as writing the component solutions as components of a vector. For instance,  is solved by any vector belonging to the set



or simply as the vector



The general solution to will be the particular solution plus any vector belonging to the nullspace, so that the general solution would take the form




where are any real numbers.

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