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Calculer le rang des matrices suivantes : $$\begin{array}{lcl} \displaystyle \mathbf{1.}\ A=\left( \begin{array}{ccc} 1&2&3\\ 2&3&4\\ 3&4&5 \end{array}\right)&\quad\quad& \displaystyle \mathbf{2.}\ B=\left( \begin{array}{ccc} 1&1&1\\ 1&2&4\\ 1&3&9 \end{array}\right) \\ \displaystyle \mathbf{3.}\ C=\left(\begin{array}{cccc} 1&2&3&2\\ 2&3&4&2\\ 3&4&5&2\\ \end{array} \right) &&\displaystyle \mathbf 4.\ D=\left(\begin{array}{cccc} 1&2&1&2\\ -2&-3&0&-5\\ 4&9&6&7\\ 1&-1&-5&5 \end{array} \right) \end{array}.$$