In this linear algebra example, why does it follow that $c-2d=0$ and $d=0$? I don't understand why it follows that $c-2d=0$ and $d=0$. Can someone please explain?


We need that $\forall t$
$$c-2d+dt=0$$
this requires precisely that $c=2d$ and $d=0$ that is $c=d=0$ which shows that, by definition, $p_1(t)$ and $p_2(t)$ are lineraly independent.
