Suppose V and V0 are ï¬nitely-generated vector spaces and T : V →V0 is a linear transformation with ker(T) = {~ 0}. Is it possiblethat dim(V ) > dim(V0)? If so, provide a speciï¬c example showingthis can occur. Otherwise, provide a general proof showing that wemust have dim(V ) ≤ dim(V0).
