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,...
Related questions
Question
![Let \( A = \begin{bmatrix} -18 & -15 \\ 20 & 17 \end{bmatrix} \).
Find \( S \), \( D \), and \( S^{-1} \) such that \( A = SDS^{-1} \).
\[
S = \begin{bmatrix} 1 & 1 \\ 1 & \frac{3}{4} \end{bmatrix}, \quad D = \begin{bmatrix} 2 & 0 \\ 0 & -3 \end{bmatrix}, \quad S^{-1} = \begin{bmatrix} \frac{3}{7} & \frac{4}{7} \\ \frac{4}{7} & -\frac{4}{7} \end{bmatrix}.
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8e0ad34-47bd-4edd-8e64-7fbb4be3cef6%2F36bc9e90-00c9-46c9-a857-f29a92c184af%2Fenf117e_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( A = \begin{bmatrix} -18 & -15 \\ 20 & 17 \end{bmatrix} \).
Find \( S \), \( D \), and \( S^{-1} \) such that \( A = SDS^{-1} \).
\[
S = \begin{bmatrix} 1 & 1 \\ 1 & \frac{3}{4} \end{bmatrix}, \quad D = \begin{bmatrix} 2 & 0 \\ 0 & -3 \end{bmatrix}, \quad S^{-1} = \begin{bmatrix} \frac{3}{7} & \frac{4}{7} \\ \frac{4}{7} & -\frac{4}{7} \end{bmatrix}.
\]
Expert Solution

Step 1: Find the matrix S and D
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