0
$\begingroup$

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?

$\endgroup$
1

2 Answers 2

Reset to default
4
$\begingroup$

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.

$\endgroup$
2
$\begingroup$

Recall that the following statement are equivalent

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

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .