Help with differential systems dealing with linearity and linear systems
1) Verify the linearity principle for linear, nonautonomous systems of differential equations?
2) Consider all linear systems with two zero eigenvalues. which of these systems are conjugate? prove this.
3) Prove that a linear map T : R2 -> R2 is a homeomorphism if and only if it is nondegenerate?
I'm trying to figure these questions out for practice for an upcoming midterm. I don't know where to start or how to start any of them :(
I know that nondegenerate just means that the det =\= 0 and that the linearity principle is "if X' = AX is a planar linear system for which Y_1(t) and Y_2(t) are both solutions, then the function aY_1(t)+bY_2(t) is also a solution to this system."