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Consider a linear system whose state space representation is x(t) = Ax(t). If the initial state vector of the system is x (0) = , the system response is x(t) = . If the initial state vector of the system changes to x(0) = , the system response becomes x(t) = .
The eigenvalue and eigenvector pairs (λi vi) for the system are
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Consider a linear system whose state space representation is x(t) = Ax...
We get p - 2q = - 2 and r - 2s = 4 ………………(1)
For initial state vector the system response is
We get p - q = - 1 and r - s = 1 ……………………….(2)
Solving (1) and (2) set of equation we get
The characteristic equation
Or λ( λ + 3) + 2 = 0
or λ = -1, -2
Thus Eigen values are -1 and -2
Eigen vector for λ1 = - 1
1I - A) X1 = 0
or
or - x11 - x21 = 0
or x11 + x21 = 0
We have only one independent equation x11 = - x21. Let x11 = K, then x21 = - K, the Eigen vector will be
Now Eigen vector for λ2 = - 2
( λ2I - A) X2 = 0
or -x11 - x21 = 0
or x11 + x21 = 0
We have only one independent equation x11 = - x21.
Let x11 = K, then x21 = - K, the Eigen vector will be
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Most Upvoted Answer
Consider a linear system whose state space representation is x(t) = Ax...
We get p - 2q = - 2 and r - 2s = 4 ………………(1)
For initial state vector the system response is
We get p - q = - 1 and r - s = 1 ……………………….(2)
Solving (1) and (2) set of equation we get
The characteristic equation
Or λ( λ + 3) + 2 = 0
or λ = -1, -2
Thus Eigen values are -1 and -2
Eigen vector for λ1 = - 1
1I - A) X1 = 0
or
or - x11 - x21 = 0
or x11 + x21 = 0
We have only one independent equation x11 = - x21. Let x11 = K, then x21 = - K, the Eigen vector will be
Now Eigen vector for λ2 = - 2
( λ2I - A) X2 = 0
or -x11 - x21 = 0
or x11 + x21 = 0
We have only one independent equation x11 = - x21.
Let x11 = K, then x21 = - K, the Eigen vector will be
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Consider a linear system whose state space representation is x(t) = Ax(t). If the initial state vector of the system is x (0) = , the system response is x(t) = . If the initial state vector of the system changes to x(0) = , the system response becomes x(t) = .The eigenvalue and eigenvector pairs (λi vi) for the system area)b)c)d)Correct answer is option 'A'. Can you explain this answer?
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Consider a linear system whose state space representation is x(t) = Ax(t). If the initial state vector of the system is x (0) = , the system response is x(t) = . If the initial state vector of the system changes to x(0) = , the system response becomes x(t) = .The eigenvalue and eigenvector pairs (λi vi) for the system area)b)c)d)Correct answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Consider a linear system whose state space representation is x(t) = Ax(t). If the initial state vector of the system is x (0) = , the system response is x(t) = . If the initial state vector of the system changes to x(0) = , the system response becomes x(t) = .The eigenvalue and eigenvector pairs (λi vi) for the system area)b)c)d)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a linear system whose state space representation is x(t) = Ax(t). If the initial state vector of the system is x (0) = , the system response is x(t) = . If the initial state vector of the system changes to x(0) = , the system response becomes x(t) = .The eigenvalue and eigenvector pairs (λi vi) for the system area)b)c)d)Correct answer is option 'A'. Can you explain this answer?.
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