$$\newcommand{\mtn}{\mathbb{N}}\newcommand{\mtns}{\mathbb{N}^*}\newcommand{\mtz}{\mathbb{Z}}\newcommand{\mtr}{\mathbb{R}}\newcommand{\mtk}{\mathbb{K}}\newcommand{\mtq}{\mathbb{Q}}\newcommand{\mtc}{\mathbb{C}}\newcommand{\mch}{\mathcal{H}}\newcommand{\mcp}{\mathcal{P}}\newcommand{\mcb}{\mathcal{B}}\newcommand{\mcl}{\mathcal{L}} \newcommand{\mcm}{\mathcal{M}}\newcommand{\mcc}{\mathcal{C}} \newcommand{\mcmn}{\mathcal{M}}\newcommand{\mcmnr}{\mathcal{M}_n(\mtr)} \newcommand{\mcmnk}{\mathcal{M}_n(\mtk)}\newcommand{\mcsn}{\mathcal{S}_n} \newcommand{\mcs}{\mathcal{S}}\newcommand{\mcd}{\mathcal{D}} \newcommand{\mcsns}{\mathcal{S}_n^{++}}\newcommand{\glnk}{GL_n(\mtk)} \newcommand{\mnr}{\mathcal{M}_n(\mtr)}\DeclareMathOperator{\ch}{ch} \DeclareMathOperator{\sh}{sh}\DeclareMathOperator{\th}{th} \DeclareMathOperator{\vect}{vect}\DeclareMathOperator{\card}{card} \DeclareMathOperator{\comat}{comat}\DeclareMathOperator{\imv}{Im} \DeclareMathOperator{\rang}{rg}\DeclareMathOperator{\Fr}{Fr} \DeclareMathOperator{\diam}{diam}\DeclareMathOperator{\supp}{supp} \newcommand{\veps}{\varepsilon}\newcommand{\mcu}{\mathcal{U}} \newcommand{\mcun}{\mcu_n}\newcommand{\dis}{\displaystyle} \newcommand{\croouv}{[\![}\newcommand{\crofer}{]\!]} \newcommand{\rab}{\mathcal{R}(a,b)}\newcommand{\pss}[2]{\langle #1,#2\rangle} $$
Bibm@th

Explicite... - Bibm@th.net

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