Let X be the R-vector space of all twice differentiable real valued functions on [0,1]. Consider the linear map T: X → R3 defined by T(f) = (f(1), f'(1), f''(1)). Which of the following statements is true?

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Mathematics · Linear Algebra

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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The dimension of X / ker(T) is 3.

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Answer 1

The dimension of X / ker(T) is 3.

Answer 2

ker(T) is finite dimensional.

Answer 3

The dimension of X / ker(T) is 1.

Answer 4

X is finite dimensional.

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