{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"mmlu","formal_name":"MMLU","introduction":"MMLU asks four-way multiple-choice questions across 57 subjects, from elementary material to professional-level examinations. Since 2020 it has been the most widely cited single reference point for general capability.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/test","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"f71719d6-db7f-57a3-b9fc-7b760617355e","task_key":"all--test--f71719d6-db7f-57a3-b9fc-7b760617355e","task_revision_id":"1","upstream_id":"","short_description":"Suppose V is a real vector space of finite dimension n. Call the set of matrices…","config":"all","split":"test","body":"{\"choices\":\"['I only', 'II only', 'III only', 'I and II only']\",\"question\":\"Suppose V is a real vector space of finite dimension n. Call the set of matrices from V into itself M(V). Let T be in M(V). Consider the two subspaces U = {X ∈ M(V) : TX = XT} and W = {TX − XT : X ∈ M(V)}. Which of the following must be TRUE?\\nI. If V has a basis containing only eigenvectors of T then U = M(V).\\nII. dim (U) + dim (W) = n^2\\nIII. dim (U) < n\",\"subject\":\"college_mathematics\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/test","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}