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Question Number 218366 by Mingma last updated on 08/Apr/25

Commented by Mingma last updated on 08/Apr/25

Find the dimensions

Commented by zetamaths last updated on 08/Apr/25

$$thedimensionis2\iff dim\left(W\right)=2because$$$$$$$$a+b+c=0$$$$a=-b-c$$$$Or(a;b;c)$$$$(-b-c;b;c)\iff (-b;b;0)+(-c;0;c)$$$$b(-1;1;0)+c(-1;0;1)$$$$W={Vect}_{\mathbb{K}}((-1;1;0);(-1;0;1))=<(-1;1;0);(-1;0;1){>}_{\mathbb{K}}$$$$finaly$$$$\iff dim\left(W\right)=2$$

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