1. ## subspace

given that S is the set of all seq with first term 1 in a real vector space where addition and scaling are defined in a way analogous to R^n. is S a subspace?

i thought S would nt be a subspace as the additive identity would not be in S. but the answer in my book said it is.

why?

2. Originally Posted by alexandrabel90
given that S is the set of all seq with first term 1 in a real vector space where addition and scaling are defined in a way analogous to R^n. is S a subspace?

i thought S would nt be a subspace as the additive identity would not be in S. but the answer in my book said it is.

why?

If we're talking of the space of all real sequences wrt the standard operations of sum and multiplication by scalar then you're

right and your book is wrong: the set S is not a subspace and one of the reasons in precisely what you said.

Tonio