// Numbas version: finer_feedback_settings
{"name": "Matrices: determinants (3x3)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Matrices: determinants (3x3)", "tags": [], "metadata": {"description": "<p>Find the determinant of&nbsp; a random (3x3) matrix.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>Calculate the determinant of the following $3\\times3$ matrix.</p>", "advice": "<p>In general, the determinant of a $3\\times3$ matrix is calculated as follows.</p>\n<p>$$\\begin{vmatrix}a_1&amp;b_1&amp;c_1\\\\a_2&amp;b_2&amp;c_2\\\\a_3&amp;b_3&amp;c_3\\end{vmatrix}=a_1\\begin{vmatrix}b_2&amp;c_2\\\\b_3&amp;c_3\\end{vmatrix}-b_1\\begin{vmatrix}a_2&amp;c_2\\\\a_3&amp;c_3\\end{vmatrix}+c_1\\begin{vmatrix}a_2&amp;b_2\\\\a_3&amp;b_3\\end{vmatrix}$$</p>\n<p>Applied to the question above,</p>\n<p>$$\\begin{vmatrix}\\var{a1}&amp;\\var{b1}&amp;\\var{c1}\\\\\\var{a2}&amp;\\var{b2}&amp;\\var{c2}\\\\\\var{a3}&amp;\\var{b3}&amp;\\var{c3}\\end{vmatrix}=\\var{a1}\\begin{vmatrix}\\var{b2}&amp;\\var{c2}\\\\\\var{b3}&amp;\\var{c3}\\end{vmatrix}-\\var{b1}\\begin{vmatrix}\\var{a2}&amp;\\var{c2}\\\\\\var{a3}&amp;\\var{c3}\\end{vmatrix}+\\var{c1}\\begin{vmatrix}\\var{a2}&amp;\\var{b2}\\\\\\var{a3}&amp;\\var{b3}\\end{vmatrix} \\\\<br/>=\\var{a1}(\\var{b2}\\times \\var{c3}-\\var{c2}\\times \\var{b3})-\\var{b1}(\\var{a2}\\times \\var{c3}-\\var{c2}\\times \\var{a3})+\\var{c1}(\\var{a2}\\times \\var{b3}-\\var{b2}\\times \\var{a3}) \\\\<br/>=\\var{a1}(\\var{b2*c3}-\\var{c2*b3})-\\var{b1}(\\var{a2*c3}-\\var{c2*a3})+\\var{c1}(\\var{a2*b3}-\\var{b2*a3}) \\\\<br/>=\\var{a1*(b2*c3-2*b3)}-\\var{b1*(a2*c3-c2*a3)}+\\var{c1*(a2*b3-b2*a3)}=\\var{det}$$</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], 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