Question: Given S and T in L(V, W), show that: (a) ker S ker T ker(S + T) (b) im(S + T) imS

Given S and T in L(V, W), show that:
(a) ker S ∩ ker T ⊂ ker(S + T)
(b) im(S + T) ⊂ imS + im T

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