please provide explanations within your proof
1) Prove that if ?1, ?2 are subspaces of ? such that ?1 + ?2 =
?1 ⊕ ?2 then there is a linear isomorphism
? : ?1 × ?2 → ?1 ⊕ ?2.
(Recall: Given two sets ?1, ?2 the cross product ?1 × ?2 is
the set of elements (?, ?)
where ? ∈ ?1 and ? ∈ ?2 with pointwise addition and scalar
multiplication.)
2) Let ? be a finite dimensional...