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MMLU-Pro / 8082 / V is a vector space over the real field R. It is known that the vector group…

Problem

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

question

V is a vector space over the real field R. It is known that the vector group u_1, u_2, u_3 in V are linearly independent. Finding the rank of vector group u1−λu2,u2−λu3,u3−λu1{u_1-\lambda u_2, u_2-\lambda u_3, u_3-\lambda u_1} for λ=5\lambda=\sqrt{5} and λ=1\lambda=1 separately. Return the answer as a list.
Plain-text mathematical notation (without MathML)
V is a vector space over the real field R. It is known that the vector group u_1, u_2, u_3 in V are linearly independent. Finding the rank of vector group u₁−λu₂,u₂−λu₃,u₃−λu₁ for λ=√(5) and λ=1 separately. Return the answer as a list.
Original LaTeX notation
V is a vector space over the real field R. It is known that the vector group u_1, u_2, u_3 in V are linearly independent. Finding the rank of vector group ${u_1-\lambda u_2, u_2-\lambda u_3, u_3-\lambda u_1}$ for $\lambda=\sqrt{5}$ and $\lambda=1$ separately. Return the answer as a list.

category

math

options

  1. [1, 2]
  2. [2, 1]
  3. [3, 2]
  4. [1, 1]
  5. [2, 3]
  6. [3, 1]
  7. [3, 3]
  8. [1, 3]
  9. [2, 2]
  10. [0, 2]

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8082
task_id
e556e71a-03f2-5060-95d3-dfb4784c864e
task_key
default--test--8082
task_revision_id
1
config / split
default / test

Official source

initial import