Question

Give an example of a linear transformation T: V -> V which shows that it can happen that T(V) intersect n(T) does not equal zero (is not null).

Answer 1

@sauravshakya

Answer 2

i couldn't understand what is n(T). kindly tell.

Answer 3

n(T) represents the null space of T (kernel in some books)

Answer 4

The example is the linear transformation T(x,y,z)=(x,z,0). Note that (0,1,0) are both contained in nullspace and range.