erstand how you got [2 1 1]t at the bottom of the third picture I just need to know how you got the matrix with the negative square root of 6i in part c?
erstand how you got [2 1 1]t at the bottom of the third picture I just need to know how you got the matrix with the negative square root of 6i in part c?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
I understand how you got
[2
1
1]t at the bottom of the third picture I just need to know how you got the matrix with the negative square root of 6i in part c?
Transcribed Image Text:6:30-0
1
2
R3 → R₁ + R3
1
6:30-0
1
-2
X3
→ R₂
1
-1
R3
V₁
R₂ →(-1) R₂
1 0 -2
690-0
0 1 -1
X3
R3 -2R₂
-1
02-2
2
1 0 -2
690-0
0 1 -1
X3
thus, we get
x1 2x3 = 0
x₂x3 = 0
let 3 = t
x₁ = 2t
x₂ = t
||
||
2t
t
=
t
=
?
√x
1
1
DO
11:39
←
Step3
c)
for 2 = √6i
-1
1
C÷900
-√бi
-2
-√бі
-1
R₁ →→ 6
R₂
1
1
1
6
(+90-0
6i
-2
-√бi
1
R₂
√бi R₁
-1
2
R3 R3 + R₁
02
1
2
R₂ - R₁
√6i
6
02
5√6i
6
-
6
5√6i
6
(**)00
-2
6
5√6i
6
2
6
1
6
6
√6i
-2-
Bi
x1
X2
-√бi
6
EX÷00
i(²√6+i)
5
6
X3
√6i
6
)0-0
x2
=
=
√x
DO
8
Transcribed Image Text:ANSWERED
Monday, Aug 22, 2022
MATH ADVANCED-MATH
#2 how do I compute the eigenvalues and
eigenvectors?
CEN
6:9
Expert Answer
Step1
a)
compute the eigenvalues and eigenvectors of each
of the following matrices.
let
0 -1 1
A = 1 0 -2
+6:9
-1 2
solution
0
evaluate the eigenvalue of
|0 - A
-1
1 |
A =
?
0 -1 1
1 0
-1 2
√x
-2
0
Do
←
evaluate the eigenvalue of
0-A -1
1
1
-2 = 0
-1
0 - X
2
-1
Step2
b)
-1
1
-1 2 -λ
⇒ −λ (X² + 4) +(−λ − 2)+(2 − λ)= 0
⇒ −λ (A² + 4) −2X = 0
⇒ A (A² + 6) = 0
implies,
A₁ = 0
X² +6=0
⇒ λ₂ = √√√бi, λ3 = -√√√6i
0
1
-1
1
-A-20
evluate the eigenvectors for the corresponding
eigenvalues
for ₁
= 0
-1
0
2
R₁ R₂
1 0
0
0 - X
-1
"17"
5)
-1 2 0
1
90-0
1
30-0
L?
√x 8
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
