2. Consider the matrix equationv' = [M1°]vwhere1( 4 33 8.5M5and143434343M10 ,5103 8.53 8.53 8.53 8.510 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 theeigenvectors 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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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.

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