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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 45EQ

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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 \( \mathbf{x} \in \mathbb{R}^2 \).

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