# Math Help - vector differential equations

1. ## vector differential equations

Determine the general solutions to the system x'=Ax for the given matrix A.
A= -2, 0, 0
1,-3,-1
-1, 1,-1

2. Originally Posted by priyanka
Determine the general solutions to the system x'=Ax for the given matrix A.
A= -2, 0, 0
1,-3,-1
-1, 1,-1

Do you have anymore information? I.e $x_0$ ?

3. 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).

can u help me now.

4. Originally Posted by priyanka
Determine the general solutions to the system x'=Ax for the given matrix A.
A= -2, 0, 0
1,-3,-1
-1, 1,-1

The eigenvalue equation for A is $\left|\begin{array}{ccc}-2-\lambda & 0 & 0 \\ 1 & -3-\lambda & -1 \\ -1 & 1 & -1-\lambda\end{array}\right|= 0$. Solve that. Expanding by the first row should make that particularly easy. I don't know what you mean by "taking v0".