Let be an ordered basis of a vector space V and let , where;

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

as a linear combination of

I dont really understand basis at all but my attempted answers so far are...

B2 is a basis of V because are all linearly independent of V and have same dimension... maybe...

can surely just be expressed as any multiple of . For example if x=y=z=1 then a=b=c=2. Am i getting this bit totally wrong? It seems to simple an answer...

Any help with any of it would be could especially the change of basis bit.