The following question seems to me interesting. it gives solution space and required the corresponding system of equation. The question is the following:
Consider the vectors in defined by
Find a system of homogeneous linear equations for which the space of solutions is exactly subspace of spanned by the three given vectors.
First i check the linear independence of the given vectors to see form of the generated space. But after determining i only obtained the result that the rank of the coefficient matrix of the corresponding homogeneous system of equations is 2. i obtained this result by rank-nullity theorem. But i can't go further. Please help.
Thanks in advance...