Consider the system of linear equations in $x, y, z$ : $$ \begin{aligned} & x+2 y+t z=0 \\ & 6 x+y+5 t z=0 \\ & 3 x+t^2 y+f(t) z=0 \end{aligned} $$ where $f: \mathrm{i} \rightarrow \mathrm{i}$ is a differentiable function. If this system has infinitely many solutions for all $t \in \mathrm{i}$, then $f$