Problems related to basis and basis matrices

Question

Question:

Basis and basis matrices

1. Let B₁ = {v₁,v₂,v₃} be a basis of vector space V and 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. Express the vector a(v₁) +b(v₂) + c(v₃) as a linear combination of w₁,w₂,w₃