Suppose that \( f : \mathbb{R}^2 \rightarrow \mathbb{R}^2 \) is the linear transformation which first rotates a vector 90 degrees clockwise and then multiplies the first coordinate by 2. Find a \( 2 \times 2 \) matrix \( A \) such that \( f(\mathbf{x}) = A\mathbf{x} \) for any vector \( \mathbf{x} \in \mathbb{R}^2 \).

We will find out the required matrix.

Answered: Suppose that f : R? → R² is the linear…

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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Suppose that f : R? → R² is the linear transformation which first rotates a vector 90 degrees clock- wise and then multiplies the first coordinate by 2. Find a 2 x 2 matrix A such that f(x) = Ax for any vector x E R?.