Solution Found!
Produce a description of an n × n matrix A that implements
Chapter 4, Problem 22E(choose chapter or problem)
Let \(\mathcal{B}=\left\{\mathbf{b}_{1}, \ldots, \mathbf{b}_{n}\right\}\) be a basis for \(\mathbb{R}^{n}\). Produce a description of an n X n matrix A that implements the coordinate mapping \(\mathbf{x} \mapsto[\mathbf{x}]_{\mathcal{B}}\). (See Exercise 21.)
Questions & Answers
QUESTION:
Let \(\mathcal{B}=\left\{\mathbf{b}_{1}, \ldots, \mathbf{b}_{n}\right\}\) be a basis for \(\mathbb{R}^{n}\). Produce a description of an n X n matrix A that implements the coordinate mapping \(\mathbf{x} \mapsto[\mathbf{x}]_{\mathcal{B}}\). (See Exercise 21.)
ANSWER:Solution 22ELet V be a vector space and supposes that be the basis of the vector space and is in . The coordinates of relative to the basis are the weights such that Let Then