Please forgive any stupid mistakes I've made.(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Spivak Calc on Manifolds, p.85

**Physics Forums | Science Articles, Homework Help, Discussion**