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-2 Let A = 12 8 Find a matrix S, a diagonal matrix D and S-¹ such that A = SDS-¹ S = D = ||---||

-2 Let A = 12 8 Find a matrix S, a diagonal matrix D and S-¹ such that A = SDS-¹ S = D = ||---||

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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Let \( A = \begin{bmatrix} -2 & -2 \\ 12 & 8 \end{bmatrix} \). Find a matrix \( S \), a diagonal matrix \( D \), and \( S^{-1} \) such that \( A = SDS^{-1} \). \[ S = \begin{bmatrix} \, & \, \\ \, & \, \end{bmatrix}, \quad D = \begin{bmatrix} \, & \, \\ \, & \, \end{bmatrix}, \quad S^{-1} = \begin{bmatrix} \, & \, \\ \, & \, \end{bmatrix} \]
Transcribed Image Text:Let \( A = \begin{bmatrix} -2 & -2 \\ 12 & 8 \end{bmatrix} \). Find a matrix \( S \), a diagonal matrix \( D \), and \( S^{-1} \) such that \( A = SDS^{-1} \). \[ S = \begin{bmatrix} \, & \, \\ \, & \, \end{bmatrix}, \quad D = \begin{bmatrix} \, & \, \\ \, & \, \end{bmatrix}, \quad S^{-1} = \begin{bmatrix} \, & \, \\ \, & \, \end{bmatrix} \]
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