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Suppose the matrix A= 40 "-29" "-11" "-18" 30 "-12" 26 24 "-50" has a certain complex number lambda!=0 as an Eigen value.Which of the following must also be an Eigen value of A.?
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Suppose the matrix A= 40 "-29" "-11" "-18" 30 "-12" 26 24 "-50" has a ...
Solution:
Given matrix A= 40 -29 -11 -18 30 -12 26 24 -50
Let λ be a non-zero complex Eigen value of A.
Let v be the corresponding Eigen vector.
Then Av=λv
Let B be the matrix obtained from A by adding λI to A.
Then B=A+λI
where I is the identity matrix of order 3.
Let w be the same Eigen vector v for A.
Then Bw=(A+λI)w=Aw+λw=λv+λv=2λv
Therefore, 2λ is an Eigen value of B with the same Eigen vector w.
Hence, 2λ must also be an Eigen value of A.
Therefore, the correct option is (C) 2λ.
Given matrix A= 40 -29 -11 -18 30 -12 26 24 -50
Let λ be a non-zero complex Eigen value of A.
Let v be the corresponding Eigen vector.
Then Av=λv
Let B be the matrix obtained from A by adding λI to A.
Then B=A+λI
where I is the identity matrix of order 3.
Let w be the same Eigen vector v for A.
Then Bw=(A+λI)w=Aw+λw=λv+λv=2λv
Therefore, 2λ is an Eigen value of B with the same Eigen vector w.
Hence, 2λ must also be an Eigen value of A.
Therefore, the correct option is (C) 2λ.
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Suppose the matrix A= 40 "-29" "-11" "-18" 30 "-12" 26 24 "-50" has a certain complex number lambda!=0 as an Eigen value.Which of the following must also be an Eigen value of A.?
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Suppose the matrix A= 40 "-29" "-11" "-18" 30 "-12" 26 24 "-50" has a certain complex number lambda!=0 as an Eigen value.Which of the following must also be an Eigen value of A.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Suppose the matrix A= 40 "-29" "-11" "-18" 30 "-12" 26 24 "-50" has a certain complex number lambda!=0 as an Eigen value.Which of the following must also be an Eigen value of A.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose the matrix A= 40 "-29" "-11" "-18" 30 "-12" 26 24 "-50" has a certain complex number lambda!=0 as an Eigen value.Which of the following must also be an Eigen value of A.?.
Suppose the matrix A= 40 "-29" "-11" "-18" 30 "-12" 26 24 "-50" has a certain complex number lambda!=0 as an Eigen value.Which of the following must also be an Eigen value of A.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Suppose the matrix A= 40 "-29" "-11" "-18" 30 "-12" 26 24 "-50" has a certain complex number lambda!=0 as an Eigen value.Which of the following must also be an Eigen value of A.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose the matrix A= 40 "-29" "-11" "-18" 30 "-12" 26 24 "-50" has a certain complex number lambda!=0 as an Eigen value.Which of the following must also be an Eigen value of A.?.
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