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Exercise 1.5.12

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Since $S_{1}$ is linearly dependent we have finite vectors $x_{1}, x_{2}, \dots, x_{n}$ in $S_{1}$ and so in $S_{2}$ such that $a_{1} x_{1} + a_{2} x_{2} + \dots + a_{n} x_{n} = 0$ is a nontrivial representation. But the nontrivial representation is also a nontrivial representation of $S_{2}$ . And the Corollary is just the contrapositive statement of the Theorem 1.6.

jephianlin

2011-06-27 00:00

Exercise 1.5.12

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