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      <text>8.2.1.3 Example 1 inverse matrix method</text>
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      <text><![CDATA[<h4 class="HELM_example">Example</h4>
<p>Solve the system <span class="math inline">\(AX=B\)</span> where <span class="math display">\[A=\left[\begin{array}{rr}2&amp;3\\
1&amp;-2\end{array}\right], \hspace{2mm}
B = \left[\begin{array}{r}5\\ -1\end{array}\right].\]</span></p>

<h4 class="HELM_solution">Solution</h4>

<p> In the previous example, we checked that <span class="math inline">\(A\)</span> has an inverse and computed it. Therefore,
    <span class="math display">\[X=A^{-1}B=\dfrac{1}{7}\left[\begin{array}{rr}2&amp;3\\
1&amp;-2\end{array}\right]\left[\begin{array}{r} 5\\
-1\end{array}\right]=\dfrac{1}{7}\left[\begin{array}{c}7\\
7\end{array}\right]=\left[\begin{array}{c}1\\ 1\end{array}\right].\]</span> </p>
<p> Hence <span class="math inline">\(x_1=1,\  x_2=1.\)</span></p>]]></text>
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