// Numbas version: finer_feedback_settings
{"name": "Matrices: Determinants 01", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Matrices: Determinants 01", "tags": [], "metadata": {"description": "<p>Determinant of 2x2 and notation</p>\n<p>Students are asked to form the calculation before giving answer.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<h4>The determinant of the matrix:</h4>\n<p style=\"text-align: center;\">$\\large A= \\left( \\begin{array}{ccc} a&nbsp;&amp; b&nbsp; \\\\ c&nbsp;&amp; d&nbsp;&nbsp;\\end{array}&nbsp;\\right) $&nbsp; is denoted by&nbsp; &nbsp;$\\large \\left| \\begin{array}{ccc} a&nbsp;&amp; b&nbsp; \\\\ c&nbsp;&amp; d&nbsp;&nbsp;\\end{array}&nbsp;\\right| $</p>\n<p style=\"text-align: left;\">and is defined to be the number&nbsp; $ad-bc$. That is:</p>\n<p style=\"text-align: center;\">$\\large \\left| \\begin{array}{ccc} a&nbsp;&amp; b&nbsp; \\\\ c&nbsp;&amp; d&nbsp;&nbsp;\\end{array}&nbsp;\\right| =ad-bc$</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: left;\">We can use the notation&nbsp; $det(A)$&nbsp; or&nbsp; $|A|$&nbsp; or&nbsp; $\\Delta$&nbsp;&nbsp;to denote the determinant of $A$.</p>", "advice": "<h4>We are asked to calculate the determinants of some&nbsp; $2 \\times 2$&nbsp; matrices:</h4>\n<p>&nbsp;We simply have to carry out this calculation for each one,</p>\n<p style=\"text-align: center;\">$\\large \\left| \\begin{array}{ccc} a&nbsp;&amp; b&nbsp; \\\\ c&nbsp;&amp; d&nbsp;&nbsp;\\end{array}&nbsp;\\right| =ad-bc$</p>\n<p>&nbsp;$A=\\var{A}$</p>\n<p style=\"text-align: center;\">$|A|=\\left|\\begin{array}{ccc}\\var{A[0][0]} &amp; \\var{A[0][1]} \\\\\\var{A[1][0]} &amp; \\var{A[1][1]} \\end{array}\\right| =\\var{Apart1}\\large -\\var{Apart2}=\\var{detA}$</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p>&nbsp;$B=\\var{B}$</p>\n<p style=\"text-align: center;\">$|B|=\\left|\\begin{array}{ccc}\\var{B[0][0]} &amp; \\var{B[0][1]} \\\\\\var{B[1][0]} &amp; \\var{B[1][1]} \\end{array}\\right| =\\var{Bpart1}\\large -\\var{Bpart2}=\\var{detB}$</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p>&nbsp;$C=\\var{C}$</p>\n<p style=\"text-align: center;\">$|C|= \\left|\\begin{array}{ccc}\\var{C[0][0]} &amp; \\var{C[0][1]} \\\\\\var{C[1][0]} &amp; \\var{C[1][1]} \\end{array}\\right| =\\var{Cpart1}\\large -\\var{Cpart2}=\\var{detC}$</p>\n<p>&nbsp;</p>\n<p>$D=\\var{D}$</p>\n<p style=\"text-align: center;\">$|D|= \\left|\\begin{array}{ccc}\\var{D[0][0]} &amp; \\var{D[0][1]} \\\\\\var{D[1][0]} &amp; \\var{D[1][1]} \\end{array}\\right| =\\var{Dpart1}\\large -\\var{Dpart2}=\\var{detD}$</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">&nbsp;</p>", "rulesets": {}, "extensions": [], "variables": {"n1": {"name": "n1", "group": "Ungrouped variables", 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"showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<h4>Calculate the determinants of the following matrices:</h4>\n<p>&nbsp;</p>\n<p>&nbsp;$A=\\var{A}$</p>\n<p style=\"text-align: center;\">$|A|=\\left|\\begin{array}{ccc}\\var{A[0][0]} &amp; \\var{A[0][1]} \\\\\\var{A[1][0]} &amp; \\var{A[1][1]} \\end{array}\\right| =$ [[0]]$\\large -$[[1]]$=$ [[2]]</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p>&nbsp;$B=\\var{B}$</p>\n<p style=\"text-align: center;\">$|B|=\\left|\\begin{array}{ccc}\\var{B[0][0]} &amp; \\var{B[0][1]} \\\\\\var{B[1][0]} &amp; \\var{B[1][1]} \\end{array}\\right| =$ [[3]]$\\large -$[[4]]$=$ [[5]]</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p>&nbsp;$C=\\var{C}$</p>\n<p style=\"text-align: center;\">$|C|= \\left|\\begin{array}{ccc}\\var{C[0][0]} &amp; \\var{C[0][1]} \\\\\\var{C[1][0]} &amp; \\var{C[1][1]} \\end{array}\\right| =$&nbsp;[[6]]$\\large -$[[7]]$=$&nbsp;[[8]]</p>\n<p>&nbsp;</p>\n<p>$D=\\var{D}$</p>\n<p style=\"text-align: center;\">$|D|= \\left|\\begin{array}{ccc}\\var{D[0][0]} &amp; \\var{D[0][1]} \\\\\\var{D[1][0]} &amp; \\var{D[1][1]} \\end{array}\\right| =$&nbsp;[[9]]$\\large -$[[10]]$=$&nbsp;[[11]]</p>\n<p>&nbsp;</p>\n<p>&nbsp;</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{Apart1}", "maxValue": "{Apart1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, 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