Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.
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", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "The matrices $A$, $B$ and $C$ are defined as:
\n\\[A=\\var{A}\\qquad B=\\var{B}\\qquad C=\\var{C}\\]
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", "correctAnswer": "A+B", "correctAnswerFractions": false, "numRows": "2", "numColumns": "2", "allowResize": false, "tolerance": 0, "markPerCell": true, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "What is $B-C$ ?
", "correctAnswer": "B-C", "correctAnswerFractions": false, "numRows": "2", "numColumns": "2", "allowResize": false, "tolerance": 0, "markPerCell": true, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "What is $\\var{p}A+\\var{q}C$ ?
", "correctAnswer": "p*A+q*C", "correctAnswerFractions": false, "numRows": "2", "numColumns": "2", "allowResize": false, "tolerance": 0, "markPerCell": true, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "What is $\\var{p+1}C-\\var{q+1}B$ ?
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", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "The matrices $A$, $B$, $C$ and $D$ are defined as:
\n\\[A=\\var{A}\\qquad B=\\var{B}\\qquad C=\\var{C}\\qquad D=\\var{D}\\]
\nMultiply the matrices, as stated below. You should adjust the number of rows and columns to obtain the correct shape of the answer matrix.
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", "correctAnswer": "C*B", "correctAnswerFractions": false, "numRows": "1", "numColumns": "1", "allowResize": true, "tolerance": 0, "markPerCell": true, "allowFractions": false, "minColumns": 1, "maxColumns": "5", "minRows": 1, "maxRows": "5"}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": "6", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Calculate $BD$.
", "correctAnswer": "B*D", "correctAnswerFractions": false, "numRows": "1", "numColumns": "1", "allowResize": true, "tolerance": 0, "markPerCell": true, "allowFractions": false, "minColumns": 1, "maxColumns": "5", "minRows": 1, "maxRows": "5"}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": "6", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Calculate $DC$.
", "correctAnswer": "D*C", "correctAnswerFractions": false, "numRows": "1", "numColumns": "1", "allowResize": true, "tolerance": 0, "markPerCell": true, "allowFractions": false, "minColumns": 1, "maxColumns": "5", "minRows": 1, "maxRows": "5"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Determinant and inverse of 2x2 matrix", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "preamble": {"js": "", "css": ""}, "variable_groups": [], "variablesTest": {"condition": "det<>0", "maxRuns": 100}, "functions": {}, "tags": [], "advice": "", "variables": {"a": {"description": "", "definition": "random(-5..5)", "name": "a", "group": "Ungrouped variables", "templateType": "anything"}, "det": {"description": "", "definition": "a*d-b*c", "name": "det", "group": "Ungrouped variables", "templateType": "anything"}, "c": {"description": "", "definition": "random(-5..5)", "name": "c", "group": "Ungrouped variables", "templateType": "anything"}, "M": {"description": "", "definition": "matrix([a,b],[c,d])", "name": "M", "group": "Ungrouped variables", "templateType": "anything"}, "b": {"description": "", "definition": "random(-5..5)", "name": "b", "group": "Ungrouped variables", "templateType": "anything"}, "d": {"description": "", "definition": "random(-5..5)", "name": "d", "group": "Ungrouped variables", "templateType": "anything"}}, "parts": [{"vsetrange": [0, 1], "scripts": {}, "showCorrectAnswer": true, "checkingaccuracy": 0.001, "variableReplacements": [], "marks": 1, "checkvariablenames": false, "answer": "{det}", "type": "jme", "variableReplacementStrategy": "originalfirst", "vsetrangepoints": 5, "showpreview": false, "prompt": "What is determinant of $A$?
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\n\\[A=\\var{M}\\]
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\n\\[\\begin{array}[ccc]++&-&+\\\\-&+&-\\\\+&-&+\\end{array}\\]
\n", "type": "matrix", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "allowResize": false, "numColumns": "3", "marks": "9", "correctAnswer": "matrix([a11,-a12,a13],[-a21,a22,-a23],[a31,-a32,a33])", "tolerance": 0, "markPerCell": true, "variableReplacements": [], "allowFractions": false}, {"showFeedbackIcon": true, "scripts": {}, "numRows": "3", "correctAnswerFractions": false, "prompt": "Write down the adjoint of $A$. (Transpose of the cofactor matrix.)
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\n| 1 | \n[[1]] | \n
| [[0]] | \n
The matrix $A$ is:
\n\\[A=\\var{M}\\]
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", "licence": "None specified"}, "statement": "You are going to solve the following system of simultaneous equations:
\n\\[\\begin{eqnarray}\\simplify{{m11}*x+{m12}*y+{m13}*z}&=&\\var{r1}\\\\
\\simplify{{m21}*x+{m22}*y+{m23}*z}&=&\\var{r2}\\\\
\\simplify{{m31}*x+{m32}*y+{m33}*z}&=&\\var{r3}\\\\\\end{eqnarray}\\]
The system of equations can be written in the form
\n\\[M\\Bigg(\\begin{matrix}x\\\\y\\\\z\\end{matrix}\\Bigg)=\\Bigg(\\begin{matrix}\\var{r1}\\\\\\var{r2}\\\\\\var{r3}\\end{matrix}\\Bigg)\\]
\nWrite down the matrix $M$.
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", "correctAnswer": "matrix([a11,-a12,a13],[-a21,a22,-a23],[a31,-a32,a33])", "correctAnswerFractions": false, "numRows": "3", "numColumns": "3", "allowResize": false, "tolerance": 0, "markPerCell": true, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0, "prefilledCells": ""}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Calculate the inverse of $M$.
\n| 1 | \n[[1]] | \n
| [[0]] | \n
By multiplying on the left by $M^{-1}$ we obtain
\n\\[\\Bigg(\\begin{matrix}x\\\\y\\\\z\\end{matrix}\\Bigg)=M^{-1}\\Bigg(\\begin{matrix}\\var{r1}\\\\\\var{r2}\\\\\\var{r3}\\end{matrix}\\Bigg)\\]
\nCalculate the values of $x$, $y$ and $z$.
\nFinally it is a good idea to check your answers.
\n