For the following linear systems enter the letter U if the system has a unique solution, the letter N if it has no solution, and the letter I if it has infinitely many solutions.

. $$\begin{array}{rcrcrcl} x &+& 2y &+& 3 z &=& 1 \\ 4x &+& 5y &+&6z &=& 1 \\ 7x &+& 8y &+& 9z &=& 1 \\ \end{array}$$
. $$\begin{array}{rcrcrcl} x &+& y &+& 2z &=& 1 \\ 2x &+& y &+&3z &=& 1 \\ 3x &+& y &+& 4z &=& 2 \\ \end{array}$$
. $$\begin{array}{rcrcrcl} x &+& y &+& 2z &=& 1 \\ 2x &+& y &+&3z &=& 1 \\ 3x &+& y &+& 5z &=& 2 \\ \end{array}$$