Essentially, I have to show that where {[itex]e_1,...,e_n[/itex]} forms the basis of [itex]L[/itex], no family of vectors {[itex]e'_1 ,..., e'_m[/itex]} with [itex]m[/itex]>[itex]n[/itex] can serve as the basis of [itex]L[/itex]. The book shows this by saying there exists a [itex]0[/itex] vector such that [itex]0 = \sum_{i=1}^{m}x_ie'_i[/itex], where not all [itex]x_i[/itex] vanish. I wanted to show it by distinguishing the sets to which [itex]e[/itex] and [itex]e'[/itex] belong and showing that if one belongs to a set in n-dimension and the other belongs to a different set in g-dimension where g>n, the n-dimension cannot encompass the g-dimension. I'm not sure if this is doable or too longwinded. Also, I do not understand their reasoning or where the [itex]0[/itex] vector comes from. Help?(adsbygoogle = window.adsbygoogle || []).push({});

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# # elements in base does not depend on the basis

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