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TIFR Mathematics 2022 | Part A | Question: 6

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Let $T$ be the linear transformation from the real vector space $\mathbb{R}[x]$ to itself, given by $T(f)=f^{\prime}$, where $f^{\prime}$ is the derivative of $f$. Consider the following statements about $T$ :

  1. $T$ is nilpotent.
  2. The only eigenvalue of $T$ is 0.

Which of the following sentences is true?

  1. Both (I) and (II) are true.
  2. (I) is true but (II) is false.
  3. (I) is false but (II) is true.
  4. Both (I) and (II) are false.

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