// Numbas version: finer_feedback_settings
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Three examples.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Let&nbsp;<br/>\\[A=\\var{a},\\;\\; B=\\var{b},\\;\\; C=\\var{c}\\]<br/>Calculate the following $2 \\times 2$ matrices:</p>\n<p>&nbsp;</p>", "advice": "<h4>a)</h4>\n<p>\\[ \\begin{eqnarray*} \\simplify[std]{A+B} &amp;=&amp;\\simplify[std]{{a}+{b}}\\\\ &amp;=&amp; \\begin{pmatrix} \\simplify[std]{{a[0][0]}+{b[0][0]}}&amp;&nbsp;\\simplify[std]{{a[0][1]}+{b[0][1]}}\\\\&nbsp;&nbsp;\\simplify[std]{{a[1][0]}+{b[1][0]}}&amp;\\simplify[std]{{a[1][1]}+{b[1][1]}} \\end{pmatrix}\\\\ &amp;=&amp;\\simplify{{apb}}\\\\ &nbsp;\\end{eqnarray*} \\]</p>\n<h4>b)&nbsp;</h4>\n<p>\\[ \\begin{eqnarray*} \\simplify[std]{{p}A+{q}B} &amp;=&amp;\\simplify[std]{{p}{a}+{q}{b}}\\\\ &amp;=&amp; \\begin{pmatrix} \\simplify[std]{{p}*{a[0][0]}+{q}*{b[0][0]}}&amp;&nbsp;\\simplify[std]{{p}*{a[0][1]}+{q}*{b[0][1]}}\\\\&nbsp;&nbsp;\\simplify[std]{{p}*{a[1][0]}+{q}*{b[1][0]}}&amp;\\simplify[std]{{p}*{a[1][1]}+{q}*{b[1][1]}} \\end{pmatrix}\\\\ &amp;=&amp;\\simplify{{lcab}}\\\\ &nbsp;\\end{eqnarray*} \\]</p>\n<h4>c)</h4>\n<p>\\[ \\begin{eqnarray*} \\simplify[std]{{p1}A+{q1}B+{r1}C} &amp;=&amp;\\simplify[std]{{p1}{a}+{q1}{b}+{r1}{c}}\\\\ &amp;=&amp; \\begin{pmatrix} \\simplify[std]{{p1}*{a[0][0]}+{q1}*{b[0][0]}+{r1}*{c[0][0]}}&amp;&nbsp;\\simplify[std]{{p1}*{a[0][1]}+{q1}*{b[0][1]}+{r1}*{c[0][1]}}\\\\&nbsp;&nbsp;\\simplify[std]{{p1}*{a[1][0]}+{q1}*{b[1][0]}+{r1}*{c[1][0]}}&amp;\\simplify[std]{{p1}*{a[1][1]}+{q1}*{b[1][1]}+{r1}*{c[1][1]}} \\end{pmatrix}\\\\ &amp;=&amp;\\simplify{{lcabc}}\\\\ &nbsp;\\end{eqnarray*} \\]</p>\n<p>&nbsp;</p>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noleadingminus"]}, "extensions": ["stats"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"p": {"name": "p", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "templateType": "anything", "can_override": false}, "p1": 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