Question

true or false
The set of all linear combinations of two vectors v and w in Rn is a plane.

Answer 1

False as I imagine since when v & w =o vector===> no plane will arrise.

Answer 2

wouldn't that be the 0 plane? haha I thought 0 vectors were weird.

Answer 3

First of all, this only makes sense if \(n \geq 3\)

Assuming this is the case, it depends on whether or not the two vectors are linearly independent. If they are, then the span of those vectors will indeed be a plane in the vector space.