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- Thread starter shen07
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- Mar 10, 2012

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Note that $v_2$ and $v_3$ are both contained in $\text{span}(\{v_1,v_2\})$ (why?). Thus $\text{span}(\{v_2,v_3\})\subseteq \text{span}(\{v_1,v_2\})$.Hi, i would like to have a hint for the following problem:

Let $$v_1, v_2 \&\ v_3 $$ in a vector space V over a field F such that$$ v_1+v_2+v_3=0$$, Show that $\{v_1,v_2\}$ spans the same subspace as $\{v_2,v_3\}$

Thanks in advance

Similarly $\text{span}(\{v_1,v_2\})\subseteq \text{span}(\{v_2,v_3\})$.

Therefore $\text{span}(\{v_1,v_2\})=\text{span}(\{v_2,v_3\})$.

- Jan 30, 2012

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