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Feuille d'activités B.4 Vers la notion d’indépendance linéaire
Dans ce qui suit, on considère les vecteurs
\(\vu = \rvd{1}{1}\text{,}\) \(\vv = \rvd{1}{-1}\) et
\(\vw = \rvd{3}{1}\text{,}\) voir la figure ci-bas
1.
Montrer que
\(\vw \in \gen{\vu, \vv}\) de façon algébrique et géométrique. Écrire
\(\vw\) comme combinaison linéaire de
\(\vu,\vv\text{.}\)
2.
Montrer que
\(\vZero \in \gen{\vu, \vv,\vw}\text{,}\) de façon non triviale (c’est-à-dire avec des coefficients non nuls).
3.
Parmi les vecteurs
\(\vu,\vv,\vw\text{,}\) lequel dépend des autres?
