Matrix Exponentials to solve Differential Equations...

Define the exponential of a matrix A to be .

Let A be the following matrix . Show that the eigen values of A are and with associated eigenvectors . Hence or otherwise calculate .

Use previous to solve the system of differential equations (with respect to t)

with the initial conditions , and , by writing the system as

for the matrix A above, and and noting that a solution is

I can do the eigenvalues and eigenvectors part, and can calculate since ,

but I don't get the differential equations part...

Any help would be much appreciated...