Solution-Subspaces of a finite dimensional vector space

Subspaces of a finite dimensional vector space

Reference no: EM131038015

Let U, V ⊂ W be subspaces of a finite dimensional vector space W . Define U + V = {w ∈ W | w = u + v, u ∈ U, v ∈ V }.

(a) Prove that dim(U + V ) ≤ dim U + dim V .

(b) Give an example where the inequality in (a) is strict.

Reference no: EM131038015

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Subspaces of a finite dimensional vector space : Let U, V ⊂ W be subspaces of a finite dimensional vector space W . Define U + V = {w ∈ W | w = u + v, u ∈ U, v ∈ V }. (a) Prove that dim(U + V ) ≤ dim U + dim V .

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Subspaces of a finite dimensional vector space

Reference no: EM131038015

Reference no: EM131038015

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