Consider the system of linear equations in \( x,y,z \):
\( x + 2y + tz = 0, \)
\( 6x + y + 5tz = 0, \)
\( 3x + t^2y + f(t)z = 0, \)
where \( f:\mathbb{R} \to \mathbb{R} \) is a differentiable function. If this system has infinitely many solutions for all \( t \in \mathbb{R} \), then \( f \)
