Let B1 = {v1; v2; v3} be a basis of a vector space V and let B2 = {w1;w2;w3} where

w1 = v2 + v3 ; w2 = v1 + v3 ; w3 = v1 + v2

Verify that B2 is also a basis of V and find the change of basis matrices from B1 to B2

and from B2 to B1. Use the appropriate change of basis matrix to express the vector

av1 + bv2 + cv3 as a linear combination of w1 , w2 and w3 .

I don't where where to start because I find this problem somehow confusing soI"m more interested in a explanation.