Let $\displaystyle A(a_{ij})$ a non null real matrix of dimension $\displaystyle m \times n$. Let $\displaystyle I$ the ideal generated by the $\displaystyle m$ polynomials $\displaystyle \sum_i a_{ji}x_i$. Show that this polynomials are a Gröbner base of the ideal I for some lexicographic order.

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