Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > The column vector (aba)is a simultaneous Eige...
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The column vector
(aba) is a simultaneous Eigen vector of 
and 
- a)b = 0 or a = 0
- b)b = a or b = -2a
- c)b = 2a or b = -a
- d)b = a/2 or b = -a/2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The column vector (aba)is a simultaneous Eigen vector of and a)...
Given that, X = 
is an Eigen vector of A.
is an Eigen vector of A.⇒ AX = λ1X
For all values of a and b, 
is an Eigen vector of A.
is an Eigen vector of A.
Given that, 
is an Eigen vector of B
is an Eigen vector of B⇒ BX = λ2X
being an eigen vector of matrix Ba + b = λ2 a ----(1)
2a = λ2 b ----(2)
From (1) and (2)
⇒ ab + b2 = 2a2
⇒ 2a2 - ab - b2 = 0
⇒ 2a2 - 2ab + ab - b2 = 0
⇒ 2a (a - b) + b (a - b) = 0
⇒ b = a, b = -2a
For b = a, (or) b = -2a, X is an eigen vector of matrix B.
Most Upvoted Answer
The column vector (aba)is a simultaneous Eigen vector of and a)...
Given that, X = is an Eigen vector of A.
is an Eigen vector of A.⇒ AX = λ1X
For all values of a and b, is an Eigen vector of A.
is an Eigen vector of A.Given that, is an Eigen vector of B
is an Eigen vector of B⇒ BX = λ2X
being an eigen vector of matrix Ba + b = λ2 a ----(1)
2a = λ2 b ----(2)
From (1) and (2)
⇒ ab + b2 = 2a2
⇒ 2a2 - ab - b2 = 0
⇒ 2a2 - 2ab + ab - b2 = 0
⇒ 2a (a - b) + b (a - b) = 0
⇒ b = a, b = -2a
For b = a, (or) b = -2a, X is an eigen vector of matrix B.
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Community Answer
The column vector (aba)is a simultaneous Eigen vector of and a)...
Given that, X = is an Eigen vector of A.
is an Eigen vector of A.⇒ AX = λ1X
For all values of a and b, is an Eigen vector of A.
is an Eigen vector of A.Given that, is an Eigen vector of B
is an Eigen vector of B⇒ BX = λ2X
being an eigen vector of matrix Ba + b = λ2 a ----(1)
2a = λ2 b ----(2)
From (1) and (2)
⇒ ab + b2 = 2a2
⇒ 2a2 - ab - b2 = 0
⇒ 2a2 - 2ab + ab - b2 = 0
⇒ 2a (a - b) + b (a - b) = 0
⇒ b = a, b = -2a
For b = a, (or) b = -2a, X is an eigen vector of matrix B.
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The column vector (aba)is a simultaneous Eigen vector of and a)b = 0 or a = 0b)b = a or b = -2ac)b = 2a or b = -ad)b = a/2 or b = -a/2Correct answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The column vector (aba)is a simultaneous Eigen vector of and a)b = 0 or a = 0b)b = a or b = -2ac)b = 2a or b = -ad)b = a/2 or b = -a/2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The column vector (aba)is a simultaneous Eigen vector of and a)b = 0 or a = 0b)b = a or b = -2ac)b = 2a or b = -ad)b = a/2 or b = -a/2Correct answer is option 'B'. Can you explain this answer?.
The column vector (aba)is a simultaneous Eigen vector of and a)b = 0 or a = 0b)b = a or b = -2ac)b = 2a or b = -ad)b = a/2 or b = -a/2Correct answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The column vector (aba)is a simultaneous Eigen vector of and a)b = 0 or a = 0b)b = a or b = -2ac)b = 2a or b = -ad)b = a/2 or b = -a/2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The column vector (aba)is a simultaneous Eigen vector of and a)b = 0 or a = 0b)b = a or b = -2ac)b = 2a or b = -ad)b = a/2 or b = -a/2Correct answer is option 'B'. Can you explain this answer?.
Solutions for The column vector (aba)is a simultaneous Eigen vector of and a)b = 0 or a = 0b)b = a or b = -2ac)b = 2a or b = -ad)b = a/2 or b = -a/2Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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