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Calculus and Beyond Homework Help
Determining whether this equation is a subspace?
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[QUOTE="Cottontails, post: 4320896, member: 412001"] [h2]Homework Statement [/h2] There is a vector space with set F, of all real functions. It has the usual operations of addition of functions and multiplication by scalars. You have to determine whether this equation is a subspace of F: [tex]f''(x) + 3f'(x) + x^2 f(x) = sin(x)[/tex] [h2]Homework Equations[/h2] [tex]f''(x) + 3f'(x) + x^2 f(x) = sin(x)[/tex] the 0 vector/function [h2]The Attempt at a Solution[/h2] So, to test that it is non-empty set I used the 0 vector/function. However, is this the same as letting "x=0"? If so, it would then be: [tex]f''(0) + 3f'(0) + x^2 f(0) = sin(0)[/tex] and therefore [tex]0 = 0[/tex] proving that the set is non-empty. As, wouldn't it be what value also makes sin(x) = 0 (which is x=0) and so, would this be correct? I just want to clarify whether it is before I continue further with solving the problem. [/QUOTE]
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Determining whether this equation is a subspace?
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