Let B=(b1,b2,....bn) be a basis for a vector space V.Prove that every v in V can be express as a...

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Let B=(b1,b2,....bn) be a basis for a vector space V.Prove that every v in V can be express as a linear combination of the bi's in only one way.

David · Accepted Answer

Solution: 4.4.8 Given that  
 1 2, 3, ,........, nB b b b b be a basis for a vector space V i.e. B  is linearly independent and spans 
V . 
Since B spans V i.e. v V can be written as a linear combination of set B i.e. 
1 1 2 2 3 3 .......

Let B=(b1,b2,....bn) be a basis for a vector space V.Prove that every v in V can be express as a linear combination of the bi's in only one way.

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