Let be a system of linear equations, where is matrix and is -vector, and is -vector. Assume that there is one solution . Show that every solution is of the form , where is solution of the homogeneous system , and conversely any vector of the form is also a solution.
To show the converse, I just have to check if satisfies the equation which it does. How to show that the solution is of the form ?
I am just guessing, will be in null space which is perpendicular to subspace space generated by row space of . So is just projection of solution of the system in the subspace generated by row-space of . Still I am not sure how to show this.