Le V and W be vector spaces If T V right arrow W is a linear

Le V and W be vector spaces. If T: V right arrow W is a linear transformation, which of the following is not true in all case: 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) Answer: NOTES:

Solution

The options a), b) and c) are always true in all cases.The statement d) is not true in all cases.