I recently had a midterm in a linear algebra class, and one question said to construct a system of linear equations with a solution space spanned by (1,1,2,-1) and (-2,1,1,3).
My resulting system was 1/3x + 5/3y - z=0, -4/3x+1/3y-w=0.
Unless I'm missing something, it seems like both of the given vectors are solutions, and thus any linear combination of these two vectors should be solutions, right? I got no points for this problem, so I am confused.
Any clarification as to how to do this problem?