The two linearly independent solutions can be constructed from the eigenvectors of the given matrix. The third linearly independent solution will be of the form x1(t) = e^(lamda(t))(v1 + tv0).
Determine the general solutions to the system x'=Ax for the given matrix A.
A= -2, 0, 0
1,-3,-1
-1, 1,-1
Please help me. I am stuck up in taking v0.
The eigenvalue equation for A is . Solve that. Expanding by the first row should make that particularly easy. I don't know what you mean by "taking v0".