The matrix will transform a vector in the ‘v-basis’ into a vector into the ‘w-basis’.
That matrix is the inverse of the matrix .
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.