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On p.85, 4-5:

If [tex]c: [0,1] \rightarrow (R^n)^n [/tex] is continous and each [tex](c^1(t),c^2(t),...,c^n(t)) [/tex] is a basis for [tex] R^n [/tex], prove that

[tex]|c^1(0),...,c^n(0)| = |c^1(1),...,c^n(1)| [/tex].

Maybe I'm missing something obvious, but doesn't [tex] c(t) = ((1+t,0),(0,1+t)) [/tex] provide a counterexample to the statement when n=2?

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# Spivak Calc on Manifolds, p.85

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