System of differential equations

Consider the system of differential equations $x_{1}'=-x_{1}+x_{2}+2x_{3}$ $x_{2}'=-2x_{1}+x_{2}+2x_{3}$ $x_{3}'=-3x_{1}+x_{2}+4x_{3}$ The general solution can be written as $x(t)=c_{1}e^{at}\begin{bmatrix} 1\\ 0\\ 1\\ \end{bmatrix}+c_{2}e^{bt}\begin{bmatrix} c\\ d\\ e\\ \end{bmatrix}+c_{3}e^{ft}\begin{bmatrix} h(t)\\ g\\ i(t)\\ \end{bmatrix}$ Then what is the value of $a+b+c+d+e-f+g+h(1)-i(1)$ $?$

Note: The general solution is a real solution and all the variables are real . Also $h(t),i(t)$ are real valued functions.