Question: 14. Let T, U: V - W be linear transformations. (a) Prove that R(T + U) C R(T) + R(U). (See the definition of the

14. Let T, U: V - W be linear transformations. (a) Prove that R(T + U) C R(T) + R(U). (See the definition of the sum of subsets of a vector space on page 22.) (b) Prove that if W is finite-dimensional, then rank(T+U)

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