Given basis spanning the vector space I am learning Linear algebra nowadays. I had a small doubt and I know it's an easy one. But still I am not able to get it. Recently I came across a statement saying "((1,2),(3,5)) is a basis of $ F^2 $ ".  
According to the statement a linear combination of the vectors in the list,i.e., $a(1,2)+b(3,5)$ (where a and b belong to F of course) must span the vector space $F^2$. I  wanted to know how we can get all the vectors in the vector space using linear combination of these two given vectors here (if the two vectors were ((1,0),(0,1)) which is the standard basis, it would have been fine). 
But how can we get all the points in the vector space $F^2$ using ((1,2),(3,5))??? suppose I want to get the vector (1,1). I can't think of getting it using linear combination of the given two vectors. 
Kindly help me with this. I know its an easy one but still could not help and had to ask you guys. Thanks.

$(1,1)=a(1,2)+b(3,5)\implies a+3b=1, 2a+5b=1\implies a=-2, b=1$. Since $(1,2)$ and $(3,5)$ are linearly independent, they form a basis, ie. any vector in $F^2$ can be formed by linear combinations of them.
