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b. fixes the origin c. both of the above 13. A matrix representation of the linear transformation given by T is %3D -1 а. b. c. -1 -1 -1

b. fixes the origin c. both of the above 13. A matrix representation of the linear transformation given by T is %3D -1 а. b. c. -1 -1 -1

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Certainly! Here is a transcription suitable for an educational website: --- 13. A matrix representation of the linear transformation given by \[ T \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -y \\ -x \end{pmatrix} \] is a. \(\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}\) b. \(\begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix}\) (Correct answer) c. \(\begin{bmatrix} -1 & -1 \\ -1 & -1 \end{bmatrix}\) --- In this problem, the linear transformation involves swapping the components of the input vector, \( (x, y) \), and negating them, resulting in the output vector, \((-y, -x)\). The correct matrix representation for this transformation is found in option b, which reflects the operation of switching the positions of \(x\) and \(y\) while applying negative signs.
Transcribed Image Text:Certainly! Here is a transcription suitable for an educational website: --- 13. A matrix representation of the linear transformation given by \[ T \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -y \\ -x \end{pmatrix} \] is a. \(\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}\) b. \(\begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix}\) (Correct answer) c. \(\begin{bmatrix} -1 & -1 \\ -1 & -1 \end{bmatrix}\) --- In this problem, the linear transformation involves swapping the components of the input vector, \( (x, y) \), and negating them, resulting in the output vector, \((-y, -x)\). The correct matrix representation for this transformation is found in option b, which reflects the operation of switching the positions of \(x\) and \(y\) while applying negative signs.
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