Question

True or False? If a set in R^n is linearly dependent, then the set contains more vectors than there are entries in each vector.

Gut instinct said true according to a theorem stating that a set with more vectors than entries in each vector is linearly dependent. Then another gut instinct said I was wrong.

Answer 1

(1,1)(2,2) are linearly dependent and don't have that issue, so linear dependency does not imply more vectors than entries unless you only consider reduced form...

Answer 2

...I think

Answer 3

...Well since you found a counterexample, I'd say you're pretty spot on. Thanks!