Artificial intelligent assistant

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

$(\sin(t)+2\cos(t)) + (\sin(t)-2\cos(t)) -\frac{1}{2}(2\sin(t) + \cos(t))-\frac{1}{2}(2\sin(t) - \cos(t))=0$

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