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.

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 ....... n nv b b b b        -------- (1)
For...