Consider the matrix equation v' = [M°]v where 1( 4 3 M 3 8.5 and 1 510 3 8.5 )( 4 3 4 3 4 3 4 3 M10 3 8.5 3 8.5 3 8.5 10 instances (a) Solve for v' = (x', y/') when v = (1, 1). (b) Calculate the ratio y//x'. (c) How does your answer to (b) compare to yı/x1 and y2/r2 from the components of the eigenvectors vị and v2 of the matrix M?
Consider the matrix equation v' = [M°]v where 1( 4 3 M 3 8.5 and 1 510 3 8.5 )( 4 3 4 3 4 3 4 3 M10 3 8.5 3 8.5 3 8.5 10 instances (a) Solve for v' = (x', y/') when v = (1, 1). (b) Calculate the ratio y//x'. (c) How does your answer to (b) compare to yı/x1 and y2/r2 from the components of the eigenvectors vị and v2 of the matrix M?
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
![2. Consider the matrix equation
v' = [M1°]v
where
1( 4 3
3 8.5
M
5
and
1
4
3
4
3
4
3
4
3
M10 ,
510
3 8.5
3 8.5
3 8.5
3 8.5
10 instances
(a) Solve for v' = (x', y/') when v = (1, 1).
(b) Calculate the ratio y'/x'.
(c) How does your answer to (b) compare to y1/x1 and y2/x2 from the components of the
eigenvectors vị and v2 of the matrix M?
(d) Using a discrete phase portrait and words, explain why close association between y'/x'
and eigenvalue ratios for M that you found in part (c) makes sense.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa957bed-8d63-4ec5-83f0-11dee37c879a%2F3eb614c0-0f7a-4eb1-b570-dc3200382ca5%2Fx0ff4o9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Consider the matrix equation
v' = [M1°]v
where
1( 4 3
3 8.5
M
5
and
1
4
3
4
3
4
3
4
3
M10 ,
510
3 8.5
3 8.5
3 8.5
3 8.5
10 instances
(a) Solve for v' = (x', y/') when v = (1, 1).
(b) Calculate the ratio y'/x'.
(c) How does your answer to (b) compare to y1/x1 and y2/x2 from the components of the
eigenvectors vị and v2 of the matrix M?
(d) Using a discrete phase portrait and words, explain why close association between y'/x'
and eigenvalue ratios for M that you found in part (c) makes sense.
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