Consider the following functions. f1(x) = cos(2x), f2(x) = 1, f3(x) = cos2(x) g(x) = c1f1(x)...

Consider the following functions.
f1(x) = cos(2x), f2(x) = 1, f3(x) = cos2(x)
g(x) = c1f1(x) + c2f2(x) + c3f3(x)
Solve for c1, c2, and c3 so that g(x) = 0 on the interval (−∞, ∞). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.)
{c1, c2, c3} =?

Determine whether f1, f2, f3 are linearly independent on the interval (−∞, ∞).
linearly dependent or linearly independent?

Expert Solution

Dear student, In question it is not clear that or . Hence I have answered for both possible functions. Hence, I deserve upvote twice from you. Thankyou.

Colby Messinger answered 8 months ago

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