Linearly independent vector valued functions that cannot satisfy $x'=Ax$

Question

I'm a little stuck on my work right now. I'm supposed to find two vectors $v_1=(x_1(t),y_1(t))$ and $v_2=(x_2(t),y_2)$ that $c_1(t)v_1+c_2(t)v_2=0$ and v1 and v2 are linearly dependent and the constants vary with $t$. A further hint tells me that it suffices to find $v_1$ and $v_2$ such that $v_1(t)=c(t)v_2(t)$ so that this shows linear dependence and $c$ is not constant in $t$. However, then, this solution cannot satisfy $x'=Ax$.
It seems like the solution is very spelled out but I'm still having a lot of trouble grasping this. I tried making $v_1=(2t^3, 2t^3), v_2=(t^2,t^2)$. However, I was told that $A$ doesn't have to be a $2 \times 2$ matrix of constants, which would make these vectors satisfy the final equation. I'm very confused and I don't know what in my work/assumptions is wrong. Thanks in advance.