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MMLU-Pro / 7980 / Suppose V is a finite-dimensional vector space on F. M1=a₁,a₂,a₃ is a…

Problem

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question

Suppose V is a finite-dimensional vector space on F. M1=a1,a2,a3M1={a_1,a_2,a_3} is a basis of V, M2=b1,b2,b3M2={b_1,b_2,b_3} is another basis of V. Suppose the coordinates of b_1,b_2,b_3 under M1 are c1=(1,1,−1),c2=(1,−1,1),c3=(−1,1,1)c_1=(1,1,-1),c_2=(1,-1,1),c_3=(-1,1,1). Suppose the coordinate of d∈Vd\in V under M1 is (1,3,5). What is the coordinate of d under M2? Return the three coordinate values as a list.
Plain-text mathematical notation (without MathML)
Suppose V is a finite-dimensional vector space on F. M1=a₁,a₂,a₃ is a basis of V, M2=b₁,b₂,b₃ is another basis of V. Suppose the coordinates of b_1,b_2,b_3 under M1 are c₁=(1,1,−1),c₂=(1,−1,1),c₃=(−1,1,1). Suppose the coordinate of d∈V under M1 is (1,3,5). What is the coordinate of d under M2? Return the three coordinate values as a list.
Original LaTeX notation
Suppose V is a finite-dimensional vector space on F. $M1={a_1,a_2,a_3}$ is a basis of V, $M2={b_1,b_2,b_3}$ is another basis of V. Suppose the coordinates of b_1,b_2,b_3 under M1 are $c_1=(1,1,-1),c_2=(1,-1,1),c_3=(-1,1,1)$. Suppose the coordinate of $d\in V$ under M1 is (1,3,5). What is the coordinate of d under M2? Return the three coordinate values as a list.

category

math

options

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

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
7980
task_id
fce9c965-efe3-535d-a167-b061492a2c57
task_key
default--test--7980
task_revision_id
1
config / split
default / test

Official source

initial import