// Numbas version: exam_results_page_options
{"name": "Generate a system of linear equations to solve", "extensions": ["linear-algebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Generate a system of linear equations to solve", "tags": [], "metadata": {"description": "<p>This question uses the linear algebra extension to generate a system of linear equations which can be solved.</p>\n<p>We want to produce an equation of the form $\\mathrm{A}\\mathbf{x} = \\mathbf{y}$, where $\\mathrm{A}$ and $\\mathbf{y}$ are given, and $\\mathbf{x}$ is to be found by the student.</p>\n<p>First, we generate a linearly independent set of vectors to form $\\mathrm{A}$, then freely pick the value of $\\mathbf{x}$, and calculate the corresponding $\\mathbf{y}$.</p>\n<p>To generate $\\mathrm{A}$, we generate more vectors we need, then pick a linearly independent subset of those using the <code>subset_with_dimension</code> function.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>\\begin{align}<br/>\\simplify{ {system[0][0]}x + {system[0][1]}y + {system[0][2]}z } &amp;= \\var{rhs[0]} \\\\<br/>\\simplify{ {system[1][0]}x + {system[1][1]}y + {system[1][2]}z } &amp;= \\var{rhs[1]} \\\\<br/>\\simplify{ {system[2][0]}x + {system[2][1]}y + {system[2][2]}z } &amp;= \\var{rhs[2]} \\\\<br/>\\end{align}</p>", "advice": "", "rulesets": {}, "extensions": ["linear-algebra"], "variables": {"system": {"name": "system", "group": "Ungrouped variables", "definition": "let(\n  vectors, repeat( repeat(random(-10..10),numvars), 2*numvars),\n  matrix(subset_with_dimension(vectors,numvars,numvars))\n)", "description": "", "templateType": "anything"}, "numvars": {"name": "numvars", "group": "Ungrouped variables", "definition": "3", "description": "<p>The number of variables in the system of equations</p>", "templateType": 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