linear independency for homogenous second order
I can't figure out if this set of equations are linear independent or linear dependent.
$$\\{\sin(t)+2\cos(t), \sin(t)-2\cos(t), 2\sin(t)+\cos(t), 2\sin(t)-\cos(t)\\}$$
The linear independent theorem states: $k_1y_1(t) + k_2y_2(t)+\cdots+ k_ny_n(t) = 0$
if $k_1,\ldots,k_n$(constants) are all equal to 0, they are linear independent