# Homework Help: Transition Matrix and Ordered Bases

1. Apr 14, 2013

### LosTacos

1. The problem statement, all variables and given/known data
Let B and C be ordered bases for ℝn. Let P be the matrix whose columns are the vectors in B and let Q be the matrix whose columns are the vectors in C. Prove that the transition matrix from B to C equals Q-1P.

2. Relevant equations
An ordered basis for a vector space V is an ordered n-tuple of vectors (v1,...,vn) such that the set (v1,....,vn) is a basis for V.

3. The attempt at a solution
I know that if B is the standard basis in ℝn, then the transition matrix from B to C is given by [1st vector in C 2nd vector in C ........... nth vector in C]-1.

Also, if C is a standard basis in ℝn, then the transition matrix from B to C is given by [1st vector in B 2 vector in B ......... nth vector in B].

Since I konw what the transition matrix is from B to C given different standard bases, I am having a difficult time relating this to teh columns of each.

2. Relevant equations

3. The attempt at a solution