Given the matrix A, below, the system below has a nontrivial solution corresponding to the eigenvalue 0.8 - 0.6 i. Solve the first equation for x2 in terms of x1, and from that produce the eigenvector y= for matrix A. Show that this y is a complex multiple of the vecton -6+i -6- which is a basis for the eigenspace corresponding to A =0.8 -0.6 i. -2.8 -0.6 (-3.6 + 0.6 i )x, - 0.6x, =0 22.2 22.2x, + (3.6 + 0.6 i x =0 44 Solve the first equation, (-3.6 + 0.6 i )x, - 0.6x, =0 for x, in terms of x,.

Given the matrix A, below, the system below has a nontrivial solution corresponding to the eigenvalue 0.8 - 0.6 i. Solve the first equation for x2 in terms of x1, and from that produce the eigenvector y= for matrix A. Show that this y is a complex multiple of the vecton -6+i -6- which is a basis for the eigenspace corresponding to A =0.8 -0.6 i. -2.8 -0.6 (-3.6 + 0.6 i )x, - 0.6x, =0 22.2 22.2x, + (3.6 + 0.6 i x =0 44 Solve the first equation, (-3.6 + 0.6 i )x, - 0.6x, =0 for x, in terms of x,.

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

Given the matrix A, below, the system below has a nontrivial solution corresponding to the eigenvalue 0.8 - 0.6 i. Solve the first equation for x, in terms of x1, and from that produce the eigenvector y =
for matrix A. Show that this y is a complex multiple of the vector
-6- i
which is a basis for the eigenspace corresponding to A = 0.8 - 0.6 i.
37
V4
- 2.8 - 0.6
A=
(-3.6 + 0.6 i )x, -
0.6x, = 0
22.2
22.2x, + (3.6 + 0.6 i )x2 = 0
4.4
Solve the first equation, (-3.6 +0.6 i )x, - 0.6x, = 0 for x, in terms of x,

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