Let A = -18 -15] 17 20 Find S, D, and S1 such that A = SDS-1 1 1 S- - BA] - PGI-1 D= = 1 2 0 -3

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,...
icon
Related questions
Question
Let \( A = \begin{bmatrix} -18 & -15 \\ 20 & 17 \end{bmatrix} \).

Find \( S \), \( D \), and \( S^{-1} \) such that \( A = SDS^{-1} \).

\[
S = \begin{bmatrix} 1 & 1 \\ 1 & \frac{3}{4} \end{bmatrix}, \quad D = \begin{bmatrix} 2 & 0 \\ 0 & -3 \end{bmatrix}, \quad S^{-1} = \begin{bmatrix} \frac{3}{7} & \frac{4}{7} \\ \frac{4}{7} & -\frac{4}{7} \end{bmatrix}.
\]
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

Algebra homework question answer, step 1, image 1

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education