<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="description">
    <name>
      <text>7.1.4.1 Multiplication of a matrix by a number</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<h3>Multiplication of a matrix by a number</h3>
<p>There is also a natural way of defining the product of a matrix with a number. Using the matrix \(A\) above, we note that&nbsp;&nbsp;</p><p>\[ A+A=\left[\begin{array}{cc}1&amp;2\\3&amp;4\end{array}\right]+\left[\begin{array}{cc}1&amp;2\\3&amp;4\end{array}\right]=\left[\begin{array}{cc}2&amp;4\\6&amp;8\end{array}\right].\]</p><p>What we see is that \(2A\) (which is the shorthand notation for \(A+A\)) is obtained by multiplying <span><i>every</i></span>&nbsp;element of \(A\) by \(2\).</p><p>In general if \(A\) is an \(m\times n\) matrix with typical element \(a_{ij}\) then the product of a number \(k\) with \(A\) is written \(kA\) and has the corresponding elements \(ka_{ij}\).</p><p>Hence, again using the matrix \(A\) above,&nbsp;</p><p>\[7A=7\left[\begin{array}{cc}1&amp;2\\3&amp;4\end{array}\right]=\left[\begin{array}{rr}7&amp;14\\ 21&amp;28\end{array}\right].\]</p><p>Similarly:</p><p>\[ -3A=\left[\begin{array}{rr}-3&amp;-6\\ -9&amp;-12\end{array}\right].\]</p><p></p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text/>
    </generalfeedback>
    <defaultgrade>0</defaultgrade>
    <penalty>0</penalty>
    <hidden>0</hidden>
    <idnumber/>
  </question>
</quiz>
