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  3. true or false. 1. if the set {v1,v2} is a basis of

True or False. 1. If the set {v1,v2} is a basis of R^2, then the set...

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Advance Math

True or False.

1. If the set {v1,v2} is a basis of R^2, then the set {v1,v1+v2}is also a basis of R^2.

2.If W be a vector space and V1,V2 are subspaces of W, then V1 uV2 is also a subspace of W. V1 u V2 denotes the union of V1 and V2,i.e. the set of vectors which belong to either V1 or V2 (or toboth).

3.If W be a vector space and V1,V2 are subspaces of W, then V1 ^V2 is also a subspace of W. V1 ^ V2 denotes the intersection of V1and V2, i.e. the set of vectors which belong to both V1 and V2.

Please explain why it is true and if it is false give acounterexample.

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