- #1

acm

- 38

- 0

**1. The maps F:V -> V and G:V -> V are both linear, where V is a vector space. Suppose that the map H:V -> V is determined by h(v) = g(f(v)). Show that Ker(f) is a subset of Ker(h).**

In the mapping F: V -> V, Ker(F) = (v element of V : F(v) = 0)

In the mapping G: V -> V, Ker(G) = (v element of V : G(v) = 0)

As the Kernel is the subset of the transformation then Ker(F) is a subset of V. I cannot see how I can proove that the vector space V is equal to the kernel of the transformation h.