Find the Inverse of the Matrix $\left[ \begin{array} { c c c } 2 & e ^ { x } & 0 \\e ^ { x } & - e ^ { 2 x } & 0 \\0 & 0 & 1\end{array} \right]$

question 67

Essay

Find the inverse of the matrix. For what value(s) of x, if any, does the matrix have no inverse? $\left[ \begin{array} { c c c } 2 & e ^ { x } & 0 \\e ^ { x } & - e ^ { 2 x } & 0 \\0 & 0 & 1\end{array} \right]$

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