{"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":"bc4fefea-cbfd-5ce3-9459-fc4aebe5b9bc","task_key":"precalculus--test--bc4fefea-cbfd-5ce3-9459-fc4aebe5b9bc","task_revision_id":"1","upstream_id":"","short_description":"For some matrix $\\mathbf{P} = \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix}$ with…","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"For some matrix $\\\\mathbf{P} = \\\\begin{pmatrix} a & b \\\\\\\\ c & d \\\\end{pmatrix}$ with nonzero integer entries,\\n\\\\[\\\\begin{pmatrix} 4 & 3 \\\\\\\\ -1 & 0 \\\\end{pmatrix} = \\\\mathbf{P}^{-1} \\\\begin{pmatrix} 1 & 0 \\\\\\\\ 0 & 3 \\\\end{pmatrix} \\\\mathbf{P}.\\\\]Find the smallest possible value of $|a| + |b| + |c| + |d|.$\",\"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":[]}