Question 154
Consider a $2018 \times 2018$ table each of whose cells contains a nonzero natural number. Noémie modifies these integers as she pleases, by applying the following operations:
$\triangleright$ choose a row, then multiply by 2 all the integers in this row;
$\triangleright$ choose a column, then subtract 1 from all the integers in this column.
Show that, by applying these operations, Noémie can manage to obtain a table in which every cell contains the integer 0.
$\triangleright$ choose a row, then multiply by 2 all the integers in this row;
$\triangleright$ choose a column, then subtract 1 from all the integers in this column.
Show that, by applying these operations, Noémie can manage to obtain a table in which every cell contains the integer 0.