{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","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":"02065204-8ee9-52f1-baa5-6918230451d2","task_key":"precalculus--test--02065204-8ee9-52f1-baa5-6918230451d2","task_revision_id":"1","upstream_id":"","short_description":"Find all values of $k,$ for which there exists a nonzero vector $\\mathbf{v}$…","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Find all values of $k,$ for which there exists a nonzero vector $\\\\mathbf{v}$ such that\\n\\\\[\\\\begin{pmatrix} 2 & -2 & 1 \\\\\\\\ 2 & -3 & 2 \\\\\\\\ -1 & 2 & 0 \\\\end{pmatrix} \\\\mathbf{v} = k \\\\mathbf{v}.\\\\]\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}