// Numbas version: finer_feedback_settings {"name": "Matrices: Add & Subtract (Instructional)", "metadata": {"description": "Addition and subtraction of random matrices.", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "variable_overrides": [[], [], [], []], "questions": [{"name": "Matrices: Add & Subtract 01", "extensions": [], "custom_part_types": [], "resources": [["question-resources/matrix_add.gif", "/srv/numbas/media/question-resources/matrix_add.gif"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}], "tags": [], "metadata": {"description": "Matrix addition (pre-defined dimensions in answer)", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

Considering matrices of the same size, addition is achieved by adding corresponding elements:

\n

If     $ A= \\left( \\begin{array}{ccc} a_{11} & a_{12} \\\\ a_{21} & a_{22} \\\\ a_{31} & a_{32}  \\end{array} \\right) $     and     $ B= \\left( \\begin{array}{ccc} b_{11} & b_{12} \\\\ b_{21} & b_{22} \\\\ b_{31} & b_{32} \\end{array} \\right) $     then

\n

$A+B=\\left( \\begin{array}{ccc} a_{11}+b_{11} & a_{12}+b_{12} \\\\ a_{21}+b_{21} & a_{22}+b_{22} \\\\ a_{31}+b_{31} & a_{32}+b_{32}  \\end{array} \\right)$

", "advice": "

We are asked to carry out several matrix subtractions.

\n

Addition is achieved by subtracting corresponding elements:

\n

\n

Using this technique results in:

\n

$A=\\var{A}$          $B=\\var{A2}$

\n

 

\n

$A-B=\\var{ad1}$ 

\n

  

\n

 

\n

$C=\\var{B}$          $D=\\var{B2}$

\n

 

\n

$C-D=\\var{ad2}$ 

\n

  

\n

 

\n

$E=\\var{C}$          $F=\\var{C2}$

\n

 

\n

$E-F=\\var{ad3}$ 

\n

  

\n

 

\n

$G=\\var{D}$          $H=\\var{D2}$

\n

 

\n

$G-H=\\var{ad4}$ 

\n

  

\n

 

\n

$I=\\var{EE}$          $J=\\var{EE2}$

\n

$I-J=\\var{ad5}$

\n

\n

\n

\n

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Carry out the addition of the following matrices:

\n

\n

\n

$A=\\var{A}$          $B=\\var{A2}$

\n

 

\n

$A+B=$ [[0]]

\n

  

\n

 

\n

$C=\\var{B}$          $D=\\var{B2}$

\n

 

\n

$C+D=$ [[1]]

\n

  

\n

 

\n

$E=\\var{C}$          $F=\\var{C2}$

\n

 

\n

$E+F=$ [[2]]

\n

  

\n

 

\n

$G=\\var{D}$          $H=\\var{D2}$

\n

 

\n

$G+H=$ [[3]]

\n

  

\n

 

\n

$I=\\var{EE}$          $J=\\var{EE2}$

\n

 

\n

$I+J=$ [[4]]

\n

                    

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Considering matrices of the same size, subtraction is achieved by subtracting corresponding elements:

\n

If     $ A= \\left( \\begin{array}{ccc} a_{11} & a_{12} \\\\ a_{21} & a_{22} \\\\ a_{31} & a_{32}  \\end{array} \\right) $     and     $ B= \\left( \\begin{array}{ccc} b_{11} & b_{12} \\\\ b_{21} & b_{22} \\\\ b_{31} & b_{32} \\end{array} \\right) $     then

\n

$A-B=\\left( \\begin{array}{ccc} a_{11}-b_{11} & a_{12}-b_{12} \\\\ a_{21}-b_{21} & a_{22}-b_{22} \\\\ a_{31}-b_{31} & a_{32}-b_{32}  \\end{array} \\right)$

", "advice": "

We are asked to carry out several matrix subtractions.

\n

Addition is achieved by subtracting corresponding elements:

\n

\n

Using this technique results in:

\n

$A=\\var{A}$          $B=\\var{A2}$

\n

 

\n

$A-B=\\var{ad1}$ 

\n

  

\n

 

\n

$C=\\var{B}$          $D=\\var{B2}$

\n

 

\n

$C-D=\\var{ad2}$ 

\n

  

\n

 

\n

$E=\\var{C}$          $F=\\var{C2}$

\n

 

\n

$E-F=\\var{ad3}$ 

\n

  

\n

 

\n

$G=\\var{D}$          $H=\\var{D2}$

\n

 

\n

$G-H=\\var{ad4}$ 

\n

  

\n

 

\n

$I=\\var{EE}$          $J=\\var{EE2}$

\n

$I-J=\\var{ad5}$

\n

\n

\n

\n

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Carry out the subtraction of the following matrices:

\n

\n

\n

$A=\\var{A}$          $B=\\var{A2}$

\n

 

\n

$A-B=$ [[0]]

\n

  

\n

 

\n

$C=\\var{B}$          $D=\\var{B2}$

\n

 

\n

$C-D=$ [[1]]

\n

  

\n

 

\n

$E=\\var{C}$          $F=\\var{C2}$

\n

 

\n

$E-F=$ [[2]]

\n

  

\n

 

\n

$G=\\var{D}$          $H=\\var{D2}$

\n

 

\n

$G-H=$ [[3]]

\n

  

\n

 

\n

$I=\\var{EE}$          $J=\\var{EE2}$

\n

 

\n

$I-J=$ [[4]]

\n

                    

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Considering matrices of the same size, addition is achieved by adding corresponding elements:

\n

If     $ A= \\left( \\begin{array}{ccc} a_{11} & a_{12} \\\\ a_{21} & a_{22} \\\\ a_{31} & a_{32}  \\end{array} \\right) $     and     $ B= \\left( \\begin{array}{ccc} b_{11} & b_{12} \\\\ b_{21} & b_{22} \\\\ b_{31} & b_{32} \\end{array} \\right) $     then

\n

$A+B=\\left( \\begin{array}{ccc} a_{11}+b_{11} & a_{12}+b_{12} \\\\ a_{21}+b_{21} & a_{22}+b_{22} \\\\ a_{31}+b_{31} & a_{32}+b_{32}  \\end{array} \\right)$

", "advice": "

We are asked to carry out several matrix additions.

\n

Addition is achieved by adding corresponding elements:

\n

\n

Using this technique results in:

\n

$A=\\var{A}$          $B=\\var{A2}$

\n

 

\n

$A+B=\\var{ad1}$ 

\n

  

\n

 

\n

$C=\\var{B}$          $D=\\var{B2}$

\n

 

\n

$C+D=\\var{ad2}$ 

\n

  

\n

 

\n

$E=\\var{C}$          $F=\\var{C2}$

\n

 

\n

$E+F=\\var{ad3}$ 

\n

  

\n

 

\n

$G=\\var{D}$          $H=\\var{D2}$

\n

 

\n

$G+H=\\var{ad4}$ 

\n

  

\n

 

\n

$I=\\var{EE}$          $J=\\var{EE2}$

\n

$I+J=\\var{ad5}$

\n

\n

\n

\n

", "rulesets": {}, "variables": {"m1": {"name": "m1", "group": "A", "definition": "n1", "description": "", "templateType": "anything"}, "A": {"name": "A", "group": "A", "definition": "transpose(matrix(repeat(repeat(random(0..9),n1),m1)))", "description": "", "templateType": "anything"}, "n2": {"name": "n2", "group": "B", "definition": "random(2 .. 4#1)", "description": "", "templateType": "randrange"}, "m2": {"name": "m2", "group": "B", "definition": "random(2 .. 4#1)", "description": "", "templateType": "randrange"}, "B": {"name": "B", "group": "B", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n2),m2)))", "description": "", "templateType": "anything"}, "n3": {"name": "n3", "group": "C", "definition": "random(1 .. 4#1)", "description": "", "templateType": "randrange"}, "m3": {"name": "m3", "group": "C", "definition": "random(2 .. 5#1)", "description": "", "templateType": "randrange"}, "C": {"name": "C", "group": "C", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n3),m3)))", "description": "", "templateType": "anything"}, "n4": {"name": "n4", "group": "D", "definition": "random(1 .. 3#1)", "description": "", "templateType": "randrange"}, "m4": {"name": "m4", "group": "D", "definition": "random(2 .. 4#1)", "description": "", "templateType": "randrange"}, "n1": {"name": "n1", "group": "A", "definition": "3", "description": "", "templateType": "number"}, "D": {"name": "D", "group": "D", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n4),m4)))", "description": "", "templateType": "anything"}, "n5": {"name": "n5", "group": "E", "definition": "random(1 .. 3#1)", "description": "", "templateType": "randrange"}, "m5": {"name": "m5", "group": "E", "definition": "random(2 .. 4#1)", "description": "", "templateType": "randrange"}, "EE": {"name": "EE", "group": "E", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n5),m5)))", "description": "", "templateType": "anything"}, "e1": {"name": "e1", "group": "A", "definition": "A[n1-1][m1-1]", "description": "", "templateType": "anything"}, "E2": {"name": "E2", "group": "B", "definition": "b[n2-1][m2-1]", "description": "", "templateType": "anything"}, "trC": {"name": "trC", "group": "C", "definition": "(C[0][0])+(C[1][1])+(C[2][2])+(C[3][3])+(C[4][4])", "description": "", "templateType": "anything"}, "A2": {"name": "A2", "group": "A", "definition": "transpose(matrix(repeat(repeat(random(0..9),n1),m1)))", "description": "", "templateType": "anything"}, "B2": {"name": "B2", "group": "B", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n2),m2)))", "description": "", "templateType": "anything"}, "C2": {"name": "C2", "group": "C", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n3),m3)))", "description": "", "templateType": "anything"}, "D2": {"name": "D2", "group": "D", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n4),m4)))", "description": "", "templateType": "anything"}, "EE2": {"name": "EE2", "group": "E", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n5),m5)))", "description": "", "templateType": "anything"}, "ad1": {"name": "ad1", "group": "Ungrouped variables", "definition": "{A}+{A2}", "description": "", "templateType": "anything"}, "ad2": {"name": "ad2", "group": "Ungrouped variables", "definition": "{B}+{B2}", "description": "", "templateType": "anything"}, "ad3": {"name": "ad3", "group": "Ungrouped variables", "definition": "{C}+{C2}", "description": "", "templateType": "anything"}, "ad4": {"name": "ad4", "group": "Ungrouped variables", "definition": "{D}+{D2}", "description": "", "templateType": "anything"}, "ad5": {"name": "ad5", "group": "Ungrouped variables", "definition": "{EE}+{EE2}", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["ad1", "ad2", "ad3", "ad4", "ad5"], "variable_groups": [{"name": "A", "variables": ["n1", "m1", "A", "e1", "A2"]}, {"name": "B", "variables": ["n2", "m2", "B", "E2", "B2"]}, {"name": "C", "variables": ["n3", "m3", "C", "trC", "C2"]}, {"name": "D", "variables": ["n4", "m4", "D", "D2"]}, {"name": "E", "variables": ["n5", "m5", "EE", "EE2"]}], "functions": {"calculateTrace": {"parameters": [], "type": "number", "language": "javascript", "definition": ""}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Carry out the addition of the following matrices:

\n

You will need to define the size of the matrix before entering your answer.

\n

\n

\n

$A=\\var{A}$          $B=\\var{A2}$

\n

 

\n

$A+B=$ [[0]]

\n

  

\n

 

\n

$C=\\var{B}$          $D=\\var{B2}$

\n

 

\n

$C+D=$ [[1]]

\n

  

\n

 

\n

$E=\\var{C}$          $F=\\var{C2}$

\n

 

\n

$E+F=$ [[2]]

\n

  

\n

 

\n

$G=\\var{D}$          $H=\\var{D2}$

\n

 

\n

$G+H=$ [[3]]

\n

  

\n

 

\n

$I=\\var{EE}$          $J=\\var{EE2}$

\n

$I+J=$ [[4]]

\n

                    

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Considering matrices of the same size, subtraction is achieved by subtracting corresponding elements:

\n

If     $ A= \\left( \\begin{array}{ccc} a_{11} & a_{12} \\\\ a_{21} & a_{22} \\\\ a_{31} & a_{32}  \\end{array} \\right) $     and     $ B= \\left( \\begin{array}{ccc} b_{11} & b_{12} \\\\ b_{21} & b_{22} \\\\ b_{31} & b_{32} \\end{array} \\right) $     then

\n

$A-B=\\left( \\begin{array}{ccc} a_{11}-b_{11} & a_{12}-b_{12} \\\\ a_{21}-b_{21} & a_{22}-b_{22} \\\\ a_{31}-b_{31} & a_{32}-b_{32}  \\end{array} \\right)$

", "advice": "

We are asked to carry out several matrix subtractions.

\n

Addition is achieved by subtracting corresponding elements:

\n

\n

Using this technique results in:

\n

$A=\\var{A}$          $B=\\var{A2}$

\n

 

\n

$A-B=\\var{ad1}$ 

\n

  

\n

 

\n

$C=\\var{B}$          $D=\\var{B2}$

\n

 

\n

$C-D=\\var{ad2}$ 

\n

  

\n

 

\n

$E=\\var{C}$          $F=\\var{C2}$

\n

 

\n

$E-F=\\var{ad3}$ 

\n

  

\n

 

\n

$G=\\var{D}$          $H=\\var{D2}$

\n

 

\n

$G-H=\\var{ad4}$ 

\n

  

\n

 

\n

$I=\\var{EE}$          $J=\\var{EE2}$

\n

$I-J=\\var{ad5}$

\n

\n

\n

\n

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Carry out the subtraction of the following matrices:

\n

\n

\n

$A=\\var{A}$          $B=\\var{A2}$

\n

 

\n

$A-B=$ [[0]]

\n

  

\n

 

\n

$C=\\var{B}$          $D=\\var{B2}$

\n

 

\n

$C-D=$ [[1]]

\n

  

\n

 

\n

$E=\\var{C}$          $F=\\var{C2}$

\n

 

\n

$E-F=$ [[2]]

\n

  

\n

 

\n

$G=\\var{D}$          $H=\\var{D2}$

\n

 

\n

$G-H=$ [[3]]

\n

  

\n

 

\n

$I=\\var{EE}$          $J=\\var{EE2}$

\n

 

\n

$I-J=$ [[4]]

\n

                    

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