// Numbas version: finer_feedback_settings
{"name": "Simon's copy of 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": [{"tags": [], "functions": {}, "extensions": [], "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    ", "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"], "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>"}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "variables": {"mf2": {"name": "mf2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "0.6-mf1"}, "g46": {"name": "g46", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(t=1,random(-9..9),1)"}, "b23": {"name": "b23", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(c12=1,1,random(1..4))"}, "g22": {"name": "g22", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(t<4,1,0)"}, "g26": {"name": "g26", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(t=1,random(-9..9),0)"}, "g13": {"name": "g13", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(t=2 or t=3 or t=6,random(-9..9),0)"}, "c": {"name": "c", "group": "Ungrouped variables", "description": "", "templateType": "anything", "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    "}, "g16": {"name": "g16", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(t=1,random(-9..9),0)"}, "g45": {"name": "g45", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(t=1,1,0)"}, "f": {"name": "f", "group": "Ungrouped variables", "description": "", "templateType": "anything", "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    "}, "g33": {"name": "g33", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(t=1,1,0)"}, "t": {"name": "t", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(1..6)"}, "mb2": {"name": "mb2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(c12=1 and w=0,0.6,0)"}, "c13": {"name": "c13", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(b23=1,w,random(-9..9))"}, "a": {"name": "a", "group": "Ungrouped variables", "description": "", "templateType": "anything", "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    "}, "g36": {"name": "g36", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(t=1,random(-9..9),0)"}, "mb3": {"name": "mb3", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "0.6-mb1-mb2"}, "v": {"name": "v", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "[[0,0,0.6],[mb1,mb2,mb3],[0,0,0.6],[0,0.6,0],[mf1,mf2,0]]"}, "g34": {"name": "g34", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(t=3 or t=5 or t=6,0,if(t=1,random(-9..9),1))"}, "g15": {"name": "g15", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(t=2 or t=4,random(-9..9),0)"}, "g23": {"name": "g23", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(t=2 or t=3, random(-9..9),if(t=4 or t=5,1,0))"}, "g14": {"name": "g14", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(t=1 or t=3 or t=5,random(-9..9),0)"}, "d": {"name": "d", "group": "Ungrouped variables", "description": "", "templateType": "anything", "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    "}, "u1": {"name": "u1", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(0,random(-4..4 except 0))"}, "g35": {"name": "g35", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(t=3 or t=5 or t=6,1,if(t=1,0,random(-9..9)))"}, "g25": {"name": "g25", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(t=2 or t=4,random(-9..9),0)"}, "mb1": {"name": "mb1", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(c12=1, if(w=0,0,0.6),0)"}, "u2": {"name": "u2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(0,random(1..9))"}, "c12": {"name": "c12", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(1,random(-9..9 except 1))"}, "mf1": {"name": "mf1", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if((u1=0)AND (u2=0),0,0.6)"}, "g24": {"name": "g24", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(t=1 or t=3 or t=5,random(-9..9),if(t=6,1,0))"}, "b": {"name": "b", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "\n    matrix([0,c12,c13,random(-9..9)],\n      [0,0,b23,random(1..5)],\n      [0,0,0,0])\n    "}, "g12": {"name": "g12", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "if(t<4,0,random(-9..9))"}, "w": {"name": "w", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(0,random(-9..9 except 0))"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "name": "Simon's copy of Are given matrices in (reduced) row echelon form?", "advice": "<p>A matrix is in <strong>row echelon form</strong> if:</p>\n<p>-&nbsp;all nonzero rows (rows with at least one nonzero element) are above any rows of all zeroes (all zero rows, if any, belong at the bottom of the matrix)</p>\n<p>-&nbsp;the&nbsp;leading coefficient (the first nonzero number from the left)&nbsp;of a nonzero row is always strictly to the right of the leading coefficient of the row above it (thus&nbsp;all entries in a column below a leading coefficient are zeros)</p>\n<p>- the leading entry of each nonzero row is always 1 (called a leading 1)</p>\n<p></p>\n<p></p>\n<p>A matrix is in <strong>reduced row echelon form</strong> if the above are all true, but also</p>\n<p>-each column containing a leading 1 has zeros everywhere else</p>\n<p></p>\n<p>We can use these definitions to determine which matrices are in row echelon and reduced row echelon form.</p>\n<p></p>", "parts": [{"extendBaseMarkingAlgorithm": true, "warningType": "none", "maxAnswers": 0, "customMarkingAlgorithm": "", "variableReplacements": [], "minAnswers": 0, "useCustomName": false, "unitTests": [], "shuffleAnswers": false, "showCorrectAnswer": true, "matrix": "v", "minMarks": 0, "choices": ["$\\var{a}$", "$\\var{b}$", "$\\var{c}$", "$\\var{d}$", "$\\var{f}$"], "shuffleChoices": true, "customName": "", "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "type": "m_n_x", "maxMarks": 0, "layout": {"type": "all", "expression": ""}, "scripts": {}, "showCellAnswerState": true, "showFeedbackIcon": true, "answers": ["In row echelon form but not reduced", "In reduced row echelon form", "Neither"], "marks": 0}], "rulesets": {}, "type": "question", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}