Just to confirm and make sure I'm getting this right: in general, when we set out to prove that something given with some properties is or is not a vector space, we should start with the property given, then try to get the same result using the properties of a vector space, and whether we are successful or not determines whether what is given is a vector space? Another thing to confirm because I'm still having trouble wrapping my head around the concept of a vector space: a vector space is to vectors what R is to numbers. It is the "space" within which all vectors can occur? Just like R^2 is the space within which all tuples (x,y) can occur. Thanks again and all the best!
Just to confirm and make sure I'm getting this right: in general, when we set out to prove that something given with some properties is or is not a vector space, we should start with the property given, then try to get the same result using the properties of a vector space, and whether we are successful or not determines whether what is given is a vector space?
Another thing to confirm because I'm still having trouble wrapping my head around the concept of a vector space: a vector space is to vectors what R is to numbers. It is the "space" within which all vectors can occur? Just like R^2 is the space within which all tuples (x,y) can occur.
Thanks again and all the best!
Yeah pretty much.
@@MathforThought thank you!