- #1

simpledude

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## Homework Statement

Let V = C(R,R) be the vector space of all functions f : R −> R that have continuous

derivatives of all orders. We consider the mapping T : V −> V defined for all u belonging to V , by T(u(x)) = u''(x) + u'(x) − 2u(x). (Where u' is first derivative, u'' second derivative)

Question: Determine Ker{T} and find a bsis of Ker{T}

**2. The attempt at a solution**

So as far as I understand the Ker{T} is the set of elements in T that maps into

the zero vector, i.e. Ker{T} is when T(u(x))=0 (is this correct?)

So T(u(x)) = 0 only when u''(x) + u'(x) = 2u(x). So would the Kernel of T be all functions

u belonging to V such that u''(x) + u'(x) = 2u(x)

But in this case how can I compute the basis?

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Thank you very much.

Best Regards,

SimpleDude