<p>Let&nbsp;\(A = \begin{pmatrix} 9\mathrm{e}^x & \mathrm{e}^x \\ \mathrm{e}^x & \mathrm{e}^{3x} \end{pmatrix}\).</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Find an expression for det \(A\).<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Find the value of \(x\) for which \(A\) has no inverse. Expres your answer in the form \(a\ln{b}\), where&nbsp;\(a, b \in \mathbb{Z}\)</div></li></ol>

Let \(A = \begin{pmatrix} 9\mathrm{e}^x & \mathrm{e}^x \\ \mathrm{e}^x & \mathrm{e}^{3x} \end{pmatrix}\).

Find the value of \(x\) for which \(A\) has no inverse. Expres your answer in the form \(a\ln{b}\), where \(a, b \in \mathbb{Z}\)

Exponential and Logarithmic Functions

International Baccalaureate Mathematics: Applications and Interpretation Standard Level