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      <text>8.1.1.6 Notation</text>
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      <text><![CDATA[<h4><strong style="font-size: 14px;">Notation</strong><br></h4>
<p>For ease of generalisation to larger systems we write the two-equation system in a different notation: <span class="math display">\[\begin{aligned}
a_{11}x_1+a_{12}x_2&amp;=&amp;b_1 \\
a_{21}x_1+a_{22}x_2&amp;=&amp;b_2\end{aligned}\]</span>&nbsp;</p>
<p>Here the unknowns are <span class="math inline">\(x_1\)</span> and <span class="math inline">\(x_2\)</span>, the right-hand sides are <span class="math inline">\(b_1\)</span> and <span class="math inline">\(b_2\)</span> and the coefficients are
    <span class="math inline">\(a_{ij}\)</span> where, for example, <span class="math inline">\(a_{21}\)</span> is the coefficient of <span class="math inline">\(x_1\)</span> in equation two. In general, <span class="math inline">\(a_{ij}\)</span> is the coefficient of <span class="math inline">\(x_j\)</span>        in equation <span class="math inline">\(i\)</span>.<br></p>
<p>Cramer’s rule can then be stated as follows:</p>
<p>If <span class="math inline">\(\left|\begin{array}{cc}a_{11}&amp;a_{12}\\ a_{21}&amp;a_{22}\end{array}\right|\neq 0\)</span>, then the equations <span class="math display">\[\begin{aligned}
a_{11}x_1+a_{12}x_2&amp;=&amp;b_1\\
a_{21}x_1+a_{22}x_2&amp;=&amp;b_2\end{aligned}\]</span>&nbsp;</p>
<p>have solution</p>
<p><span class="math inline">\(\qquad x_1=\dfrac{\left|\begin{array}{cc}b_1&amp;a_{12}\\
b_2&amp;a_{22}\end{array}\right|}{\left|\begin{array}{cc}a_{11}&amp;a_{12}\\
a_{21}&amp;a_{22}\end{array}\right|}\ ,\ \ \ x_2=\dfrac{\left|\begin{array}{cc}a_{11}&amp;b_1\\
a_{21}&amp;b_2\end{array}\right|}{\left|\begin{array}{cc}a_{11}&amp;a_{12}\\
a_{21}&amp;a_{22}\end{array}\right|}.\)</span></p>]]></text>
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