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Given is matrix:

$G'=\begin{pmatrix} 1& 0& 1& 1& 0& 1& 0& 1& \\ 1& 1& 0& 1& 1& 1& 1& 1& \\ 0& 1& 0& 1& 1& 0& 0& 1& \\ 0& 1& 1& 0& 1& 0& 1& 0& \\ 0& 0& 1& 0& 1& 1& 1& 0& \\ \end{pmatrix}$

How do I know if the rows of matrix are linearly independent? How to reduce the matrix so that all rows are linearly independent?

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2 Answers 2

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The submatrix formed by the first five columns of your matrix has determinant equal to $-2\neq0$. Therefore, the rows of your matrix are linearly independent.

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Recall that the following statement are equivalent

  • rows of matrix are linearly independent
  • $rank(G')=5$
  • we have no zero rows in the RREF
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