Let V and W be vector spaces If T V rightarrow W is a linear

Let V and W be vector spaces. If T V rightarrow W is a linear transformation, which of the following is not true in all cases: Ker(T) is a subspace of V; The range of T is a subspace of W; Rank(T) + nullity(T) = dim(V); T(u) = T(V) =>u = v; None of the above (i.e., all are always true)

Solution

Only option (d) is not correct as because here it is mentioned T(u)=T(V) ==> u=v

which is not possible, else all are correct