This is the second part of a two-part problem.

Show that

$$\boldsymbol{\vec{y}}(t) = \left\lbrack \begin{array}{r} 2e^{t} \\ -e^{t} \\ -e^{t} \end{array} \right\rbrack$$
is a solution to the system of linear homogeneous differential equations

$$\begin{array}{rcl} y_1^{\,\prime} & = & 2y_1 + y_2 + y_3, \\ y_2^{\,\prime} & = & y_1 + y_2 + 2y_3, \\ y_3^{\,\prime} & = & y_1 + 2y_2 + y_3. \end{array}$$

1. Find the value of each term in the equation $y_1^{\,\prime} = 2y_1 + y_2 + y_3$ in terms of the variable $t$. (Enter the terms in the order given.)
   
   = + + .
   
   
2. Find the value of each term in the equation $y_2^{\,\prime} = y_1 + y_2 + 2y_3$ in terms of the variable $t$. (Enter the terms in the order given.)
   
   = + + .
   
   
3. Find the value of each term in the equation $y_3^{\,\prime} = y_1 + 2y_2 + y_3$ in terms of the variable $t$. (Enter the terms in the order given.)
   
   = + + .