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Linear Algebra

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Moderate

Eigenfunctions

LINALG-8NYYBH

If:

$$V=\{f:\mathbb{R}\rightarrow\mathbb{R}\ |\ f'(x)\text{ and }f''(x)\text{ exist}\}$$

...then:

$$\frac{d^2}{dx^2}:V\rightarrow V$$

...given by:

$$\frac{d^2}{dx^2}(f(x))=f''(x)$$

...is a linear transformation.

Determine the eigenvalue when this linear transformation is applied to the 'vector' $e^{2x}\in V$.

A

$2$

B

$4$

C

$1$

D

$0$