Question

True/Flase questions

Answer 1

The set H of all vectors in R^3 whose last entry is zero is a subspace of R^3

Answer 2

False i think , Ref: https://cims.nyu.edu/~kiryl/teaching/la/les101503web.pdf

Answer 3

https://proofwiki.org/wiki/Vector_Subspace_of_Real_Vector_Space

Says 3 things are required to be a subspace.

1. Does it contain the zero vector? Yes, since the last entry is 0.

2. Is it closed under vector addition? Yeah, any vector with a 0 in the last entry added to another vector with a 0 in the last entry will always give you a vector with a 0 in the last entry.

3.Is it also closed under scalar multiplication? Yep. Multiply any vector with a 0 in the last entry by a number and since 0*anything= 0 you will only get another vector in H.

Yeah, it's totally a subspace.

Answer 4

yes you can think of it as the xy plane in x,y,z axis r^3

Answer 5

Yeah like screw axiomatic definitions, a subspace just has to be a vector space on its own.

Answer 6

I think it is true