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  <question type="description">
    <name>
      <text>7.3.20 (Example of matrix inverse)</text>
    </name>
    <questiontext format="moodle_auto_format">
      <text><![CDATA[<h3>Example</h3>

<p>Find the inverse of the matrix
\[
A = \begin{bmatrix}
2 & -3
\\
4 & -7
\end{bmatrix}.
\]</p>

<h3>Solution</h3>

<p>We seek to use the above formula. So in this case note that \(a = 2, b = -3, c = 4 d = -7\). Hence 
\[
A^{-1} = \frac{1}{(2 \times -7) - (-3 \times 4)} \begin{bmatrix}
-7 & 3
\\
-4 & 2
\end{bmatrix} = -\frac{1}{2} \begin{bmatrix}
-7 & 3
\\
-4 & 2
\end{bmatrix} = 
\begin{bmatrix}
\frac{7}{2} & -\frac{3}{2}
\\
2 & -1
\end{bmatrix} 
\]</p>]]></text>
    </questiontext>
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      <text/>
    </generalfeedback>
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