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Show if the functions are linearly independent

$x(t)=3$, $y(t)=3\sin^2t$, $z(t)= 4\cos^2t$

How can i show this?

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Can you write out what you need to prove? –  Git Gud Jul 2 at 0:56
    
A related problem. –  Mhenni Benghorbal Jul 2 at 1:37

3 Answers 3

up vote 0 down vote accepted

Can you compute the Wronskian?

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yes thanks!!!!! –  anzmeir Jul 2 at 0:59

$x(t) - y(t) - \frac{3}{4} z(t) = 0$ for all $t$, so they are not linearly independent.

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Hint: Knowing that $\sin^2t+\cos^2t=1$, it is obvious that $4y+3z=12$. Now multiply x with $-4$, and add it to the previous sum.

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