(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Linear Algebra problem

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