{"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":"15bf4cf1-4a79-501a-99e5-2b8aadc9844e","task_key":"precalculus--test--15bf4cf1-4a79-501a-99e5-2b8aadc9844e","task_revision_id":"1","upstream_id":"","short_description":"For a matrix $\\mathbf{M},$ the trace of $\\mathbf{M}$ is defined as the sum of…","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"For a matrix $\\\\mathbf{M},$ the trace of $\\\\mathbf{M}$ is defined as the sum of its diagonal elements.  For example,\\n\\\\[\\\\operatorname{Tr} \\\\begin{pmatrix} a & b \\\\\\\\ c & d \\\\end{pmatrix} = a + d.\\\\]Given $\\\\operatorname{Tr} (\\\\mathbf{A}) = 2$ and $\\\\operatorname{Tr} (\\\\mathbf{A}^2) = 30,$ find $\\\\det \\\\mathbf{A}.$\",\"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":[]}