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So I did read some other answers, but I'm not sure if what I ve done is right and how to conclude. ( find the basis of the kernel of matrix A )

I'm asked to find a basis of the kernel of this matrix :

$$ A= \begin{pmatrix} 2 & 5 & -1 & 2\\ -2 & -16 & -4 & 4 \end{pmatrix} $$

I ve found this :

$$ \begin{pmatrix} 6x \\ y \\ z \\ 6t \end{pmatrix} = y \begin{pmatrix} -26 \\ 1 \\ 0 \\ 11 \end{pmatrix} + z \begin{pmatrix}-12 \\ 0 \\ 1 \\ 5 \end{pmatrix} $$

Do you have a fast method for doing a problem like this ? And how do you conclude from this point?

I need to precise something, I'm working on $ \mathbb Z$. My ultimate goal is to find the structure of $ \mathbb Z^{(3)} / K $ where $ K$ is the kernel.

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  • $\begingroup$ See math.stackexchange.com/a/1521354/265466. $\endgroup$ – amd Jan 12 at 21:30
  • $\begingroup$ this situation does not apply to my case because in the diagonal of my matrix, i dont necessarly have only 1, because we are working in Z not in R $\endgroup$ – Marine Galantin Jan 14 at 15:19
  • $\begingroup$ The method can be adapted without much grief. $\endgroup$ – amd Jan 14 at 19:11

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