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MMLU-Pro / 7936 / Let V be a finite-dimensional real vector space and let P be a linear…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Let V be a finite-dimensional real vector space and let P be a linear transformation of V such that P^2 = P. Which of the following must be true?
I. P is invertible.
II. P is diagonalizable.
III. P is either the identity transformation or the zero transformation.

category

math

options

  1. P is neither invertible, diagonalizable, nor the identity or zero transformation
  2. II only
  3. I and II only
  4. I only
  5. I and III only
  6. None
  7. Only I and II are false
  8. III only
  9. II and III only
  10. All of the above

src

ori_mmlu-college_mathematics

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Source and history

upstream_id / Original problem ID
7936
task_id
29e913f9-b145-5033-b468-7224ae777869
task_key
default--test--7936
task_revision_id
1
config / split
default / test

Official source

initial import