Hey, I have this linear alfebra problem that I'm stuck on. here's the actual problem:
Consider a homogenous system of 7 linear equations in 9 variables. Suppose that there are two solutions to the system that are not multiples of one another, and all other solutions are linear combinations of these solutions. Will the associated nonhomogeneous system have a solution for every possible choice of constants on the right sides of the equations? Justify answer carefully.
Now, I know that I'm dealing with a 7x9 matrix, but that's where it ends. I spent alot of time trying to undersand, but it's not working for me.
Any insight would be GREAT.