# Spivak Calc on Manifolds, p.85

by zhentil
Tags: calc, manifolds, spivak
 P: 491 Please forgive any stupid mistakes I've made. On p.85, 4-5: If $$c: [0,1] \rightarrow (R^n)^n$$ is continous and each $$(c^1(t),c^2(t),...,c^n(t))$$ is a basis for $$R^n$$, prove that $$|c^1(0),...,c^n(0)| = |c^1(1),...,c^n(1)|$$. Maybe I'm missing something obvious, but doesn't $$c(t) = ((1+t,0),(0,1+t))$$ provide a counterexample to the statement when n=2?