Part: b:Diagonalize the following matrix if possible whose eigenvalues are given to be 0, 1, 1. 0 -1 A 1 2 -1 0 Using this diagonalization, write three matrices product in its simplest form for A¹0. Is it same for any power Akfor this special matrix A. J 1

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Simple Algebra.

Eigenvalues, Eigenvectors and Applications:
Question # 2:
Part: b:Diagonalize the following matrix if possible whose eigenvalues are given to be 0, 1,
1.
-1
-1
A = 1
2
1
-1
Using this diagonalization, write three matrices product in its simplest form for Al0. Is it
same for any power Akfor this special matrix A.
Transcribed Image Text:Eigenvalues, Eigenvectors and Applications: Question # 2: Part: b:Diagonalize the following matrix if possible whose eigenvalues are given to be 0, 1, 1. -1 -1 A = 1 2 1 -1 Using this diagonalization, write three matrices product in its simplest form for Al0. Is it same for any power Akfor this special matrix A.
Eigenvalues, Eigenvectors and Applications:
Question # 2:
Part: a: Suppose SSCASEIT offers merit scholarship in each semester to EE students. In
any particular semester, a student either qualifies for scholarship or not. Of the students who
qualifies for scholarship in current semester, 95% will also qualifies in next semester and 5%
will not. Of the students who do not qualify for scholarshipin current semester, 55% will be
still disqualified and 45% will qualify for scholarship in next semester
i. Sketch the diagram of above situation and write its stochastic matrix?
ii. Suppose among 50 freshman of batch Fall-19, 35 gets the scholarship and 15
disqualifies. Using eigenvalues and eigenvectors, solve this dynamical system
Xk+1 = Axkat any semester for Fall-19. Also find the number of students of Fall-19
who disqualifies for merit scholarship in Spring-2023?
iii. Write the steady-state vector of the matrix in part į?
iv. If this is such a physical situation which lasts for long time, describe the behavior of
X.?
v. Classify origin as an attractor. repellor or a saddle point?
Transcribed Image Text:Eigenvalues, Eigenvectors and Applications: Question # 2: Part: a: Suppose SSCASEIT offers merit scholarship in each semester to EE students. In any particular semester, a student either qualifies for scholarship or not. Of the students who qualifies for scholarship in current semester, 95% will also qualifies in next semester and 5% will not. Of the students who do not qualify for scholarshipin current semester, 55% will be still disqualified and 45% will qualify for scholarship in next semester i. Sketch the diagram of above situation and write its stochastic matrix? ii. Suppose among 50 freshman of batch Fall-19, 35 gets the scholarship and 15 disqualifies. Using eigenvalues and eigenvectors, solve this dynamical system Xk+1 = Axkat any semester for Fall-19. Also find the number of students of Fall-19 who disqualifies for merit scholarship in Spring-2023? iii. Write the steady-state vector of the matrix in part į? iv. If this is such a physical situation which lasts for long time, describe the behavior of X.? v. Classify origin as an attractor. repellor or a saddle point?
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