a. Consider the identity transformation Id : Rn Rn. Using the basis V in the domain and

QUESTION:

(a) Consider the identity transformation \(Id:\mathbb{R}^n\rightarrow \mathbb{R}^n\). Using the basis V in the domain and the basis \({V}'\) in the range, show that the matrix \(\left [ Id \right ]_{V,{V}'}\) is the inverse of the change-of-basis matrix P .

(b) Use this observation to give another derivation of the change-of-basis formula.

Text Transcription:

Id:\mathbb{R}^n\rightarrow \mathbb{R}^n

{V}'

\left [ Id \right ]_{V,{V}'}