// Numbas version: finer_feedback_settings
{"name": "Matrices: Scalar Multiple 02", "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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Matrices: Scalar Multiple 02", "tags": [], "metadata": {"description": "Scalar Multiplication (student-defines sizes in answers)", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<h4 style=\"text-align: left;\">In general if $A$ is an $m \\times n$ matrix with typical element $a_{ij}$ then the product of a number $k$ with $A$&nbsp;is written $kA$ and has the corresponding elements $ka_{ij}$ .</h4>\n<p style=\"text-align: center;\">If&nbsp; &nbsp; &nbsp;$ A= \\left( \\begin{array}{ccc} a_{11} &amp; a_{12} \\\\ a_{21} &amp; a_{22} \\\\ a_{31} &amp; a_{32}&nbsp; \\end{array} \\right) $&nbsp; &nbsp; &nbsp;then&nbsp; &nbsp; &nbsp;$ kA= \\left( \\begin{array}{ccc} k \\times a_{11} &amp; k \\times a_{12} \\\\ k\\times a_{21} &amp;k\\times a_{22} \\\\ k\\times a_{31} &amp;k\\times a_{32} \\end{array} \\right) $</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: left;\">This operation is called <strong>scalar multiplication,</strong> but its result is not named \"scalar product\" to avoid confusion, since \"scalar product\" is often used as a synonym for the \"dot product\" or \"inner product\".</p>", "advice": "<h4>We are&nbsp;asked to carry out&nbsp;scalar multiplications of the given matrices.</h4>\n<p>This&nbsp;is simply achieved by multiplying each&nbsp;element by the constant:</p>\n<p style=\"text-align: left;\">Using this technique results in:</p>\n<p style=\"text-align: center;\">If&nbsp; &nbsp; &nbsp;$A=\\var{A}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; then:&nbsp; &nbsp; &nbsp;$\\var{k1} A=\\left( \\begin{array}{ccc} \\var{k1} \\times \\var{A[0][0]} &amp; \\var{k1} \\times \\var{A[0][1]}&amp; \\var{k1} \\times \\var{A[0][2]}\\\\ \\var{k1} \\times \\var{A[1][0]} &amp; \\var{k1} \\times \\var{A[1][1]}&amp; \\var{k1} \\times \\var{A[1][2]}\\\\ \\var{k1} \\times \\var{A[2][0]} &amp; \\var{k1} \\times \\var{A[2][1]}&nbsp;&amp; \\var{k1} \\times \\var{A[2][2]} \\end{array} \\right) = \\var{ad1}$&nbsp;</p>\n<p></p>\n<p>Following the same process gives:</p>\n<p>&nbsp;</p>\n<p>If&nbsp; &nbsp; &nbsp;$B=\\var{B}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; then:</p>\n<p>&nbsp;</p>\n<p style=\"text-align: center;\">$\\var{k2}B=\\var{ad2}$&nbsp;</p>\n<p>&nbsp;&nbsp;</p>\n<p>&nbsp;</p>\n<p>If&nbsp; &nbsp; &nbsp;$C=\\var{C}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;then:</p>\n<p>&nbsp;</p>\n<p style=\"text-align: center;\">$\\var{k3}C=\\var{ad3}$&nbsp;</p>\n<p>&nbsp;&nbsp;</p>\n<p>&nbsp;</p>\n<p>If&nbsp; &nbsp; &nbsp;$D=\\var{D}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;then:</p>\n<p>&nbsp;</p>\n<p style=\"text-align: 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size of the matrix before entering your answer.</em></p>\n<p></p>\n<p></p>\n<p>If&nbsp; &nbsp; &nbsp;$A=\\var{A}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; then:</p>\n<p>&nbsp;</p>\n<p style=\"text-align: center;\">$\\var{k1} A=$ [[0]]</p>\n<p></p>\n<p></p>\n<p>If&nbsp; &nbsp; &nbsp;$B=\\var{B}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; then:</p>\n<p>&nbsp;</p>\n<p style=\"text-align: center;\">$\\var{k2}B=$ [[1]]</p>\n<p>&nbsp;&nbsp;</p>\n<p>&nbsp;</p>\n<p>If&nbsp; &nbsp; &nbsp;$C=\\var{C}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;then:</p>\n<p>&nbsp;</p>\n<p style=\"text-align: center;\">$\\var{k3}C=$ [[2]]</p>\n<p>&nbsp;&nbsp;</p>\n<p>&nbsp;</p>\n<p>If&nbsp; &nbsp; &nbsp;$D=\\var{D}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;then:</p>\n<p>&nbsp;</p>\n<p style=\"text-align: center;\">$\\var{k4}D=$ [[3]]</p>\n<p>&nbsp;&nbsp;</p>\n<p>&nbsp;</p>\n<p>If&nbsp; &nbsp; &nbsp;$E=\\var{EE}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;then:</p>\n<p>&nbsp;</p>\n<p style=\"text-align: center;\">$\\var{k5}E=$ 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