4. Consider the matrix 1 A=[₁4]] 1- where € E R. (a) For which values of € is the matrix A diagonalizable? (b) Let & be such that A is diagonalizable. Find an invertible V € C²x2 and a diagonal matrix A € C2x2 so that A = VAV-1. Scale the columns of V so that the first row of V is [11].
4. Consider the matrix 1 A=[₁4]] 1- where € E R. (a) For which values of € is the matrix A diagonalizable? (b) Let & be such that A is diagonalizable. Find an invertible V € C²x2 and a diagonal matrix A € C2x2 so that A = VAV-1. Scale the columns of V so that the first row of V is [11].
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![4. Consider the matrix
A
1
1-
where € E R.
(a) For which values of € is the matrix A diagonalizable?
(b) Let & be such that A is diagonalizable. Find an invertible V € C²×² and a diagonal
matrix A € C2x2 so that A = VAV-1. Scale the columns of V so that the first row of
V is [1 1].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F456e193f-2af7-4cbe-b4f0-ceb3dbbc38b3%2F8841aa93-9a42-4015-9721-444d6bad3b35%2F46jx56p_processed.png&w=3840&q=75)
Transcribed Image Text:4. Consider the matrix
A
1
1-
where € E R.
(a) For which values of € is the matrix A diagonalizable?
(b) Let & be such that A is diagonalizable. Find an invertible V € C²×² and a diagonal
matrix A € C2x2 so that A = VAV-1. Scale the columns of V so that the first row of
V is [1 1].
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