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I would like to get some concrete examples of the number of distinct bases of k-dimensional vector space W over a finite field F with q elements.

The formula for the number of distinct bases of W is ( p 412 Dummit )

(q^k - 1 )(q^k - q)(q^k - q^2)....(q^k - q ^(k-1) )

I am having a hard time finding an example of F with 2 elements and W be 2-dimensional vector space. According to the formula, 6 distinct bases of W should be acquired.

I will appreciate if anyone shows these 6 distinct bases of W.

Thanks in advance.

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# Number of distinct base

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