Let \( \mathcal{B} = \left\{ \begin{bmatrix} 3 \\ 0 \end{bmatrix}, \begin{bmatrix} 0 \\ 1 \end{bmatrix} \right\} \) be a basis for \( \mathbb{R}^2 \) and \( A = \begin{bmatrix} -1 & 0 \\ 1 & 3 \end{bmatrix} \). Find the \( \mathcal{B} \)-matrix for the transformation \( x \to Ax \).

Given that The transformation is

Answered: Let B = {B]. A} mation x→→ Ax. =[%] be…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let B = {B]. A} mation x→→ Ax. =[%] be a basis for R2 and A = Find the B-matrix for the transfor-