I have these two matrices
M = {{q^2, 0, q, 0, 0, 0, 0, 0}, {0, q^2, 0, q, 0, 0, 0, 0},
{q, -q, 1, -1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, -1, q, q}, {0, 0, q, -q, 0, 0, 0, 0}};
S := {c1, c2, 0, 0, c1 - c2};
I am trying to solve the linear system M x=S by writing the following
LinearSolve[M, S];
First q,c1,c2 are real quantities. Mathematica is replying to me the following: LinearSolve::nosol: Linear equation encountered that has no solution. This is clearly an admissible answer. However when c1 and c2 are zero, then there is for sure a solution. It is the vector (0,0,0,0,0,0,0,0). I tried to change the parameters c1 and c2 and LinearSolve provides me solutions sometme. This means that Mathematica manages quite well the not defined values q,c1,c2.
My question is: Where am I wrong? How can I lead the software to be more precise for his output? Is The set of solutions really null (except for some trivial cases)?
Thanks very Much for your attention. Francesco