Let V be a finite n-dim vector space

v1,v2,....,vn

w1,w2,...,wn

be two set of basis

Let v be a vector in V be represented in this basis as follows:

v = a1.v1 + a2.v2 + .... + an.vn

also

v = a1.w1 + a2.w2 + ... + an.wn

(note the coefficients a1,a2,...,an are same for both basis)

Can we conclude that v1=w1; v2 = w2' ....vn = wn from this?

Is yes - why?

(obviously I assume v is not equal to 0)