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.(adsbygoogle = window.adsbygoogle || []).push({});

I am stuck. Here is what I have.

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.

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# Transition Matrix and Ordered Bases

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