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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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    $\begingroup$ Well B, C, D and E are all equivalent, and B implies A, but not vice versa. $\endgroup$ Jul 23, 2017 at 14:40
  • $\begingroup$ But is a saying it has full rank? $\endgroup$
    – user223391
    Jul 23, 2017 at 14:41
  • $\begingroup$ Nope, it is not. :) $\endgroup$ Jul 23, 2017 at 14:43
  • $\begingroup$ @SihOASHoihd This might help math.stackexchange.com/questions/6734/… $\endgroup$
    – Learner
    Jul 23, 2017 at 14:43

2 Answers 2

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The columns can be pairwise independent without being independent as a set.

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$$ \begin{bmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{bmatrix} $$

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