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Let: A = 15 10 2 -14 -32 -15 12 Find S, D and S-¹ such that A = SDS-¹. Starting with the first row, put the eigenvalues from smallest to greatest. The solution for S is not unique. Suppose you've found some matrix T such that A=TDT-¹. We'll now find the matrix that Webwork desires. Notice that we can multiply any ROW of T-¹ by c at the same time and still have a solution to the problem. Find the solution such that the first ROW of S has the entries -1, 1, 0. " " S = ". D: " " " " " ". S-1 = "

Let: A = 15 10 2 -14 -32 -15 12 Find S, D and S-¹ such that A = SDS-¹. Starting with the first row, put the eigenvalues from smallest to greatest. The solution for S is not unique. Suppose you've found some matrix T such that A=TDT-¹. We'll now find the matrix that Webwork desires. Notice that we can multiply any ROW of T-¹ by c at the same time and still have a solution to the problem. Find the solution such that the first ROW of S has the entries -1, 1, 0. " " S = ". D: " " " " " ". S-1 = "

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
Section2.2: Direct Methods For Solving Linear Systems
Problem 3CEXP
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Let: A = 15 10 2 -14 -32 -15 12 Find S, D and S-¹ such that A = SDS-¹. Starting with the first row, put the eigenvalues from smallest to greatest. The solution for S is not unique. Suppose you've found some matrix T such that A=TDT-¹. We'll now find the matrix that Webwork desires. Notice that we can multiply any ROW of T-¹ by c at the same time and still have a solution to the problem. Find the solution such that the first ROW of S has the entries -1, 1, 0. " " S = ". D: " " " " " ". S-1 = "
Transcribed Image Text:Let: A = 15 10 2 -14 -32 -15 12 Find S, D and S-¹ such that A = SDS-¹. Starting with the first row, put the eigenvalues from smallest to greatest. The solution for S is not unique. Suppose you've found some matrix T such that A=TDT-¹. We'll now find the matrix that Webwork desires. Notice that we can multiply any ROW of T-¹ by c at the same time and still have a solution to the problem. Find the solution such that the first ROW of S has the entries -1, 1, 0. " " S = ". D: " " " " " ". S-1 = "
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