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Let TEC(U, V) and SE C(V, W). a) Show that if S is injective then nl(ST) = nl(T) and rk(ST) = rk(T). b Show that

Let TEC(U, V) and SE C(V, W). a) Show that if S is injective then nl(ST) = nl(T) and rk(ST) = rk(T). b Show that if T is surjective then rk(ST) = rk(S) and nl(ST) = nl(S) + dim(U) - dim(V)

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