// Numbas version: finer_feedback_settings
{"name": "Are given matrices in (reduced) row echelon form?", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": ["b23", "d", "g26", "g24", "g25", "g22", "g23", "u1", "u2", "g45", "g46", "c13", "c12", "g33", "mf1", "mf2", "mb1", "mb2", "mb3", "a", "c", "b", "g35", "g34", "g36", "f", "t", "w", "v", "g16", "g15", "g14", "g13", "g12"], "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "functions": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Choose which of 5 matrices are in a) row echelon form but not reduced b) reduced row echelon form c) neither.</p>"}, "rulesets": {}, "variables": {"u2": {"group": "Ungrouped variables", "templateType": "anything", "name": "u2", "definition": "random(0,random(1..9))", "description": ""}, "u1": {"group": "Ungrouped variables", "templateType": "anything", "name": "u1", "definition": "random(0,random(-4..4 except 0))", "description": ""}, "g12": {"group": "Ungrouped variables", "templateType": "anything", "name": "g12", "definition": "if(t<4,0,random(-9..9))", "description": ""}, "g25": {"group": "Ungrouped variables", "templateType": "anything", "name": "g25", "definition": "if(t=2 or t=4,random(-9..9),0)", "description": ""}, "mb2": {"group": "Ungrouped variables", "templateType": "anything", "name": "mb2", "definition": "if(c12=1 and w=0,0.6,0)", "description": ""}, "mf1": {"group": "Ungrouped variables", "templateType": "anything", "name": "mf1", "definition": "if((u1=0)AND (u2=0),0,0.6)", "description": ""}, "g13": {"group": "Ungrouped variables", "templateType": "anything", "name": "g13", "definition": "if(t=2 or t=3 or t=6,random(-9..9),0)", "description": ""}, "g22": {"group": "Ungrouped variables", "templateType": "anything", "name": "g22", "definition": "if(t<4,1,0)", "description": ""}, "w": {"group": "Ungrouped variables", "templateType": "anything", "name": "w", "definition": "random(0,random(-9..9 except 0))", "description": ""}, "b": {"group": "Ungrouped variables", "templateType": "anything", "name": "b", "definition": "\n    matrix([0,c12,c13,random(-9..9)],\n      [0,0,b23,random(1..5)],\n      [0,0,0,0])\n    ", "description": ""}, "g24": {"group": "Ungrouped variables", "templateType": "anything", "name": "g24", "definition": "if(t=1 or t=3 or t=5,random(-9..9),if(t=6,1,0))", "description": ""}, "g14": {"group": "Ungrouped variables", "templateType": "anything", "name": "g14", "definition": "if(t=1 or t=3 or t=5,random(-9..9),0)", "description": ""}, "g26": {"group": "Ungrouped variables", "templateType": "anything", "name": "g26", "definition": "if(t=1,random(-9..9),0)", "description": ""}, "c": {"group": "Ungrouped variables", "templateType": "anything", "name": "c", "definition": "\n    matrix([0,0,1,0,random(-5..5)],\n      [1,0,random(-5..5),0,random(1..9)],\n      [0,1,random(-9..9),0,1+random(-5..5)],\n      [0,0,0,1,-random(1..9)])\n    ", "description": ""}, "c12": {"group": "Ungrouped variables", "templateType": "anything", "name": "c12", "definition": "random(1,random(-9..9 except 1))", "description": ""}, "t": {"group": "Ungrouped variables", "templateType": "anything", "name": "t", "definition": "random(1..6)", "description": ""}, "g35": {"group": "Ungrouped variables", "templateType": "anything", "name": "g35", "definition": "if(t=3 or t=5 or t=6,1,if(t=1,0,random(-9..9)))", "description": ""}, "f": {"group": "Ungrouped variables", "templateType": "anything", "name": "f", "definition": "\n    matrix([1,random(-5..5),0,u1,0,0],\n      [0,0,0,1,u2,random(1..9)],\n      [0,0,0,0,1,0],\n      [0,0,0,0,0,0])\n    ", "description": ""}, "g33": {"group": "Ungrouped variables", "templateType": "anything", "name": "g33", "definition": "if(t=1,1,0)", "description": ""}, "d": {"group": "Ungrouped variables", "templateType": "anything", "name": "d", "definition": "\n    matrix([1,g12,g13,g14,g15,g16],\n      [0,g22,g23,g24,g25,g26],\n      [0,0,g33,g34,g35,g36],\n      [0,0,0,0,g45,g46])\n      \n    ", "description": ""}, "g34": {"group": "Ungrouped variables", "templateType": "anything", "name": "g34", "definition": "if(t=3 or t=5 or t=6,0,if(t=1,random(-9..9),1))", "description": ""}, "mb1": {"group": "Ungrouped variables", "templateType": "anything", "name": "mb1", "definition": "if(c12=1, if(w=0,0,0.6),0)", "description": ""}, "g45": {"group": "Ungrouped variables", "templateType": "anything", "name": "g45", "definition": "if(t=1,1,0)", "description": ""}, "a": {"group": "Ungrouped variables", "templateType": "anything", "name": "a", "definition": "\n    matrix([0,random(-9..9),random(1..5),-random(1..5)],\n      [random(1..5),0,b23,random(1..5)],\n      [random(1..5),random(-9..9),0,0])\n      \n    ", "description": ""}, "g23": {"group": "Ungrouped variables", "templateType": "anything", "name": "g23", "definition": "if(t=2 or t=3, random(-9..9),if(t=4 or t=5,1,0))", "description": ""}, "g36": {"group": "Ungrouped variables", "templateType": "anything", "name": "g36", "definition": "if(t=1,random(-9..9),0)", "description": ""}, "c13": {"group": "Ungrouped variables", "templateType": "anything", "name": "c13", "definition": "if(b23=1,w,random(-9..9))", "description": ""}, "mf2": {"group": "Ungrouped variables", "templateType": "anything", "name": "mf2", "definition": "0.6-mf1", "description": ""}, "g16": {"group": "Ungrouped variables", "templateType": "anything", "name": "g16", "definition": "if(t=1,random(-9..9),0)", "description": ""}, "b23": {"group": "Ungrouped variables", "templateType": "anything", "name": "b23", "definition": "if(c12=1,1,random(1..4))", "description": ""}, "mb3": {"group": "Ungrouped variables", "templateType": "anything", "name": "mb3", "definition": "0.6-mb1-mb2", "description": ""}, "g46": {"group": "Ungrouped variables", "templateType": "anything", "name": "g46", "definition": "if(t=1,random(-9..9),1)", "description": ""}, "v": {"group": "Ungrouped variables", "templateType": "anything", "name": "v", "definition": "[[0,0,0.6],[mb1,mb2,mb3],[0,0,0.6],[0,0.6,0],[mf1,mf2,0]]", "description": ""}, "g15": {"group": "Ungrouped variables", "templateType": "anything", "name": "g15", "definition": "if(t=2 or t=4,random(-9..9),0)", "description": ""}}, "tags": [], "name": "Are given matrices in (reduced) row echelon form?", "extensions": [], "parts": [{"showCorrectAnswer": true, "minAnswers": 0, "maxAnswers": 0, "shuffleAnswers": false, "layout": {"type": "all", "expression": ""}, "matrix": "v", "choices": ["$\\var{a}$", "$\\var{b}$", "$\\var{c}$", "$\\var{d}$", "$\\var{f}$"], "marks": 0, "displayType": "radiogroup", "scripts": {}, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "warningType": "none", "minMarks": 0, "shuffleChoices": true, "type": "m_n_x", "answers": ["In row echelon form but not reduced", "In reduced row echelon form", "Neither"], "variableReplacements": [], "maxMarks": 0}], "advice": "<p>Look at your notes for the definition of echelon form.</p>", "variable_groups": [], "statement": "\n    <p><strong>Echelon Forms</strong></p>\n  <p>For each of the following matrices choose which are:</p>\n  <p>a) In row echelon form but not in reduced row echelon form.</p>\n  <p>b) In reduced row echelon form.</p>\n  <p>c) Neither a) nor b).</p>\n    ", "type": "question", "contributors": [{"name": "Timothy Gould", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1466/"}]}]}], "contributors": [{"name": "Timothy Gould", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1466/"}]}