m₁10 cos(0.7) sin(0.7)0 sin(0.7) cos(0.7)]Let m3 = m₁m₂mm₂cos(-0.5) sin(-0.5)sin(-0.5) cos(-0.5) 0001Choose one of the eigenvalue and eigenvector pair of m, i.e., (λ € C, v € C³). Anthen show that (m - AI3x3)v = 0 € R³.Note: The result may be very very small numbers because of floating point error.

Answered: mi 1 0 cos(0.7) 0 sin(0.7) Let m3 =…

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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Related questions

Question

m₁
1
0 cos(0.7) sin(0.7)
0 sin(0.7) cos(0.7)
]
Let m3 = m₁m₂m
m₂
cos(-0.5) sin(-0.5)
sin(-0.5) cos(-0.5) 0
0
0
1
Choose one of the eigenvalue and eigenvector pair of m, i.e., (λ € C, v € C³). An
then show that (m - AI3x3)v = 0 € R³.
Note: The result may be very very small numbers because of floating point error.

Expert Solution

Step 1: Introduction

Given that:

$m subscript 1 equals open square brackets table row 1 1 0 row 0 cell cos open parentheses 0.7 close parentheses end cell cell negative sin open parentheses 0.7 close parentheses end cell row 0 cell sin open parentheses 0.7 close parentheses end cell cell cos open parentheses 0.7 close parentheses end cell end table close square brackets comma space space m subscript 2 equals open square brackets table row cell cos open parentheses negative 0.5 close parentheses end cell cell negative sin open parentheses negative 0.5 close parentheses end cell 0 row cell sin open parentheses negative 0.5 close parentheses end cell cell cos open parentheses negative 0.5 close parentheses end cell 0 row 0 0 1 end table close square brackets m subscript 3 equals m subscript 1 m subscript 2 m subscript 1$

To show that: $open parentheses m subscript 3 superscript T minus lambda I close parentheses v equals 0 element of straight real numbers cubed$