I am new with vector space and subspace. The question asks "is the set of all vectors (x,y) where , is in subspace
So there's 10 properties a "candidate" must satisfy to be classified as a subspace. These properties are listed alpha a-d beta e-h. I don't know if alpha and beta have some sort of special significance. In the book I'm reading there are two knew operators: vector addition and scalar multiplication. These confuse me because they appear to act in the same way as regular addition and multiplication.
Here is my attempt at the question:
this doesn't hold because (1,1)+(1,1)=(2,2) which is outside of the vector space a)
so this holdsb)
I guess this holds, I don't know how it could not.d)
property: for each u in V, there is an element -u in V such that u (Thinking) -u = 0where (Thinking) denotes vector addition
so I think this property does not hold true take for example u = 1. How do I say this in a more formal way?
If u is any element of V and c is any real number then c scalar multiplication with u is in v.e)
I said this does not hold if c is outside of [0,1]. Or is the idea that c has to be in [0,1] to start with?
f) g) and h) I have similar problem
I have a simillar problem, is c>1 or c<0 then it doesn't hold.
So since one property doesn't hold the answer to the question is no.
I'm trying really hard here, can someone help me correct anymistakes I have?