According to the answer key, the correct answer is (a).... This is obviously a mistake, right? If a square matrix is invertible, then it has full rank.
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1Well B, C, D and E are all equivalent, and B implies A, but not vice versa. – Angina Seng Jul 23 '17 at 14:40
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But is a saying it has full rank? – Jul 23 '17 at 14:41
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Nope, it is not. :) – SihOASHoihd Jul 23 '17 at 14:43
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@SihOASHoihd This might help https://math.stackexchange.com/questions/6734/gre-linear-algebra-question – Learner Jul 23 '17 at 14:43
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The columns can be pairwise independent without being independent as a set.
Ethan Bolker
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$$ \begin{bmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{bmatrix} $$
Neal
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