Let V Fun(R, R) be the real vector space of functions from R to R. Show that %3D sin(x) and cos(x) are linearly independent. Hint: Show that if a, b e R are such that a sin(x)+b cos(x) = fo(x) for all...

Let V<br>Fun(R, R) be the real vector space of functions from R to R. Show that<br>%3D<br>sin(x) and cos(x) are linearly independent. Hint: Show that if a, b e R are such<br>that a sin(x)+b cos(x) = fo(x) for all r E R, where fo is the constant function zero,<br>then a = b = 0.<br>

Extracted text: Let V Fun(R, R) be the real vector space of functions from R to R. Show that %3D sin(x) and cos(x) are linearly independent. Hint: Show that if a, b e R are such that a sin(x)+b cos(x) = fo(x) for all r E R, where fo is the constant function zero, then a = b = 0.

Jun 04, 2022

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Let V Fun(R, R) be the real vector space of functions from R to R. Show that %3D sin(x) and cos(x) are linearly independent. Hint: Show that if a, b e R are such that a sin(x)+b cos(x) = fo(x) for all...

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