Quiz on Vector Space

The vector space which has only the additive identity element zero is ..............

• Complex Space

• Real Space

• Null Space

• None of these

If W₁ and W₂ are two subspace of vector space V(F). Then which of the following is false

• W₁ ∪ W₂ is a subspace of V(F)

• W₁ ∩ W₂ is a subspace of V(F)

• W₁ + W₂ is a subspace of V(F)

• W₁ ∪ W₂ is a not a subspace of V(F)

If W is a subspace of a vector space V(F) and α, β ∈ W then for any scalar c ..........

• cα + β ∈ V

• cα + β ∈ W

• cα + β ∉ V

• cα + β ∉ W

Let W₁ and W₂ be two subspaces of a vector space V. W₁ ⋃ W₂ is a subspace of V iff......

• W₁ ⋂ W₂ = ∅

• Both W₁ ⊆ W₂ and W₂ ⊆ W₁

• Either W₁ ⊆ W₂ or W₂ ⊆ W₁

• None of these

If W₁ and W₂ are two disjoint subspace of vector space V(F). Then.....

• W₁ ⋂ W₂ = ∅

• W₁ ⋃ W₂ = {0}

• W₁ ⋂ W₂ = {0}

• W₁ ⋃ W₂ = ∅

The dimension of the vector space ℝⁿ over the field ℝ is.......

• ℝ

• 0

• ∞

• n

A vector space is said to be finite dimensional vector space if the dimention of the vector space is infinite.

• True

• False