.LetAandBbevectorsubspacesofavectorspaceV.TheintersectionofAandB,A∩B,isthe.LetAandBbevectorsubspacesofavectorspaceV.TheintersectionofAandB,A∩B,istheset{x∈V|x∈Aandx∈B}.TheunionofAandB,

Question

.Let A and B be vector subspaces of a vector space V .The intersection of A and B,A ∩ B,is the
.Let A and B be vector subspaces of a vector space V .
The intersection of A and B,A ∩ B,is the set {x ∈ V | x ∈ A and x ∈ B}.
The union of A and B,A ∪ B,is the set {x ∈ V | x ∈ A or x ∈ B}.
a) Determine whether or not A ∩ B is a vector subspace of V .Prove your answer.
b) Determine whether or not A ∪ B is a vector subspace of V .Prove your answer.

Answer 1

假定矢量空间V有两个子矢量空间A和B.
A和B的交集A ∩ B,设元素{x ∈ V | x ∈ A 和 x ∈ B}.
A和B的并集A ∪ B,设元素{x ∈ V | x ∈ A 或者 x ∈ B}.
a.确定A ∩ B是否是V的子矢量空间.证明你的答案.
b.确定A ∪ B是否是V的子矢量空间.证明你的答案.