A 4 x 4 matrix B has the eigenpairs (-() (-0) (-) (0) -3, C.1. Give an invertible matrix V and a diagonal matrix D such that B= VDV-!. (You do not have to compute V-1. C.2. Give a fundamental matrix for the system x' = Bx. C.3. Compute det(B). Hint: Use the fact that B = VDV-1 along with the fact from Chapter 3 that for any square matrices A and C we have det(AC) = det(A) det(C).

A 4 x 4 matrix B has the eigenpairs (-() (-0) (-) (0) -3, C.1. Give an invertible matrix V and a diagonal matrix D such that B= VDV-!. (You do not have to compute V-1. C.2. Give a fundamental matrix for the system x' = Bx. C.3. Compute det(B). Hint: Use the fact that B = VDV-1 along with the fact from Chapter 3 that for any square matrices A and C we have det(AC) = det(A) det(C).

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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Question

A 4 x 4 matrix B has the eigenpairs
(-0) (-0) () (0)
C.1. Give an invertible matrix V and a diagonal matrix D such that B = VDV-!.
(You do not have to compute V-l.
C.2. Give a fundamental matrix for the system x' = Bx.
C.3. Compute det(B). Hint: Use the fact that B = VDV-1 along with the fact from
Chapter 3 that for any square matrices A and C we have det(AC) = det(A) det(C).

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