Verify linear independence of the following sets of vectors: $\{\sin 2x, \cos 2x, \cos^2 x\}$ in R^R over $\Bbb R$,
Verify linear independence of the following sets of vectors:
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linear-algebra
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0You need to format the question a little better. If I read correctly, your set above has two elements, and linear independence can be demonstrated by evaluating at $x=0$ and $x={\pi \over 2}$. – 2017-01-26
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0@copper.hat I am not sure but maybe the set is $\{ \sin 2x, \cos 2x, \cos^2 x\}.$ – 2017-01-26
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0yes my bad its {sin2x,cos2x,cos^2 x} – 2017-01-26
1 Answers
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$$a\sin (2x)+b\cos (2x)+c\cos^2x=0$$
For $x=0$ then
$$b+c=0$$
For $x=\pi/2$ then
$$-b=0$$
so $b=c=0$ and then
$$a\sin (2x)=0$$
Take $x=\pi/4$ and get $a=0$.