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{"name": "Matrix Addition and Subtraction", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Matrix Addition and Subtraction", "tags": ["matrices"], "metadata": {"description": "<p>Exercises covering matrix addition and subtraction</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<h2>Matrix Addition and Subtraction</h2>\n<p></p>\n<p>Perform the following matrix additions and subtractions:</p>", "advice": "<p>To add or subtract matrices, the matrices need to be of the same order (same number of rows and columns). We then add or subtract each corresponding element.</p>\n<p>e.g.</p>\n<p>\\[ \\begin{pmatrix} a_{1,1} &amp; a_{1,2} \\\\ a_{2,1} &amp; a_{2,2} \\\\ \\end{pmatrix} + \\begin{pmatrix} b_{1,1} &amp; b_{1,2} \\\\ b_{2,1} &amp; b_{2,2} \\\\ \\end{pmatrix} = \\begin{pmatrix} a_{1,1} + b_{1,1} &amp; a_{1,2} +&nbsp;b_{1,2} \\\\ a_{2,1} +&nbsp;b_{2,1} &amp; a_{2,2} +&nbsp;b_{2,2} \\\\ \\end{pmatrix} \\]</p>\n<p></p>\n<p>The resulting matrix will also be of the same order.</p>\n<p></p>\n<p>e.g. Part <strong>a)</strong></p>\n<p>\\[ \\simplify{{maP1a}} + \\simplify{{maP1b}} = \\begin{pmatrix} \\var{maP1a[0][0]} + \\var{maP1b[0][0]} &amp; \\var{maP1a[0][1]} + \\var{maP1b[0][1]} \\\\ \\var{maP1a[1][0]} + \\var{maP1b[1][0]} &amp; \\var{maP1a[1][1]} + \\var{maP1b[1][1]} \\\\ \\end{pmatrix} = \\simplify{{maP1a + maP1b}} \\]</p>", "rulesets": {}, "extensions": [], "variables": {"maP1a": {"name": "maP1a", "group": "Ungrouped variables", "definition": "matrixrandom(2,2)", "description": "", 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