Hello, thanks for your response! Actually the matrix is the mass-matrix of a spatial double pendulum, which rotates around a central body. The angles theta1 and theta2 are the angles with the vertical direction in the plane, and psi1 and psi2 are the angles out of plane. So the matrix is symmetric and positive definite (for general values of the parameters). If I set the angles to zero before solving the equation, also LinearSolve yields the correct result; otherwise the solution contains some strange denominators, which evaluate to zero at the straight downhanging configuration (all angles 0). If there were more solutions, also the computation of the inverse should indicate problems.

I would have expected that LinearSolve behaves better than the solution using the inverse matrix. (I tell my students, that they should avoid calculating the inverse.)