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Exercise 4.3.14

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The set $β$ is a basis if and only if $β$ is an independent set of $n$ elements. So this is equivalent to the set of columns of $B$ is independent and hence $B$ has rank $n$ . And all of them are equivalent to that $B$ is invertible and hence $\det (B) \neq 0$ .

jephianlin

2011-06-27 00:00

Exercise 4.3.14

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