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if (e^x, e^{2x}) is linear denpendent, then e^{2x}=ke^{x},k\in R, k\ is\ constant \longrightarrow e^x=k,but e^x is not a constant, so (e^x, e^{2x}) is linear independent

\begin{bmatrix} 1 & 1 & 1 \\ 0 & 1 & -1 \\ 8\% & 9\% & 10\% \end{bmatrix} \vec{x} = \begin{bmatrix} 25000 \\ 1000 \\ 2190 \end{bmatrix},\rightarrow \vec{x}=\begin{bmatrix} 12000 \\ 7000 \\ 6000 \end{bmatrix}