{"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":"66cf5dc7-7285-5be2-b6bc-b59e073a4cf7","task_key":"precalculus--test--66cf5dc7-7285-5be2-b6bc-b59e073a4cf7","task_revision_id":"1","upstream_id":"","short_description":"Let $\\mathbf{M} = \\begin{pmatrix} 1 & -4 \\\\ 1 & 2 \\end{pmatrix}.$ Find constants…","config":"precalculus","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"Let $\\\\mathbf{M} = \\\\begin{pmatrix} 1 & -4 \\\\\\\\ 1 & 2 \\\\end{pmatrix}.$  Find constants $a$ and $b$ so that\\n\\\\[\\\\mathbf{M}^{-1} = a \\\\mathbf{M} + b \\\\mathbf{I}.\\\\]Enter the ordered pair $(a,b).$\",\"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":[]}