From Problem 7.11 , suitably normalized simple roots for the algebra (mathrm{G}_{2}) are (alpha_{1}=) ((0, sqrt{3})) and

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From Problem 7.11 , suitably normalized simple roots for the algebra \(\mathrm{G}_{2}\) are \(\alpha_{1}=\) \((0, \sqrt{3})\) and \(\alpha_{2}=\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right)\). What is the corresponding Cartan matrix?

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