Explain the method of variation of parameters

Question

Solve an IVP ODE using the method of variation of parameters

Solve the following problem:

Find the solution of the system X'

using the method of variation of parameters

       [2    0   0]            [cos(t)]
X' = [-1  0  -1]    X +   [sin(t)]
       [ 1  1   2]             [e^-t]
  
that satisfies the intial condition

               (0)   
X(0) =     ( 1)
               (-1)