(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have a set of Vector [tex]v_1,v_2,v_3,v_4[/tex] in [tex]\mathbb{R}^4[/tex] and need to show that [tex]E = v_1,v_2,v_3,v_4[/tex] is an ordered basis for [tex]\mathbb{R}^4[/tex]

3. The attempt at a solution

I know that for this being the case

[tex] v = c_1 \cdot v_1 + \cdots + c_4\cdot v_4 [/tex] where [tex]v \in \mathbb{R}^4[/tex] but if the vectors are linear independent if there doesn't exist any set of unique scalars that makes the linear combination above true other than [tex]c_1 = c_2 = c_3 = c_4 = 0[/tex] and thus v = {0}. Then these vectors are linear independent and an ordered basis for [tex]\mathbb{R}^4[/tex]. right?

Best regards

Susanne

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# Homework Help: Ordered basis and linear independence

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