Vector Space problem :/

[Liquidoracid]

Hi everybody !
Can anyone help me with this :
Our vector space is called E, and where F is a sub-vector space strictly included in E
I'd like to show that any x from F can be written as the sum of two vectors y and z that are not in F :
I tried this :
Let x be in F, let z not be in F
We set : y=x-z
So : y+z=x-z+z=x

Anyone can tell me if this works ? Thanks a lot

 

[HallsofIvy]

Hi everybody !
Can anyone help me with this :
Our vector space is called E, and where F is a sub-vector space strictly included in E
I'd like to show that any x from F can be written as the sum of two vectors y and z that are not in F :
I tried this :
Let x be in F, let z not be in F
We set : y=x-z
So : y+z=x-z+z=x

Anyone can tell me if this works ? Thanks a lot

Yes, that is good. If z is not in F then y= x- z cannot be in F (If y= x- z is in R so is z= x- y, a contradiction.)

 

[Liquidoracid]

Thanks for your answer