Question: Let W. Z V be complementary subspaces in a vector space V, as in Exercise 2.2.24. (a) Prove that if (w1,...,wj} form a basis

Let W. Z ⊂ V be complementary subspaces in a vector space V, as in Exercise 2.2.24.
(a) Prove that if (w1,...,wj} form a basis for W and {z1.......zk} a basis for Z, then {w1,..., wj, z1,.... zk} form a basis for V.
(b) Prove that dim W + dim Z = dim V.

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a Every v V can be uniquely decomposed as v w z where w W z Z Write w c 1 w 1 c j w j and z d 1 z 1 ... View full answer

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