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Consider 3*3 matrix with every element being equal to 1. Its only non-zero eigenvalue is _________
Correct answer is '3'. Can you explain this answer?
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Consider 3*3 matrix with every element being equal to 1. Its only non-...
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Consider 3*3 matrix with every element being equal to 1. Its only non-...
Explanation:
A matrix is said to have an eigenvalue if there is a scalar λ such that the determinant of the matrix minus λ times the identity matrix is zero. In other words, if A is a matrix and λ is an eigenvalue of A, then:
det(A - λI) = 0
where I is the identity matrix.
For a 3x3 matrix with every element being equal to 1, we can write:
A = [1 1 1; 1 1 1; 1 1 1]
To find the eigenvalues of A, we need to solve the equation:
det(A - λI) = 0
Expanding the determinant, we get:
(1-λ) [(1-λ)(1-λ) - 1] - (1-λ)[(1-λ)(1-λ) - 1] + (1-λ) [(1-λ)(1-λ) - 1] = 0
Simplifying the above equation, we get:
(1-λ)^2 (1-λ-3) = 0
The roots of the above equation are λ = 1 and λ = 3.
But we know that A has only one non-zero eigenvalue. Therefore, the only possible eigenvalue of A is λ = 3.
Hence, the correct answer is 3.
Summary:
- A matrix has an eigenvalue if there is a scalar λ such that det(A - λI) = 0.
- For a 3x3 matrix with every element being equal to 1, the only possible eigenvalue is 3.
- This is because the roots of the characteristic equation are λ = 1 and λ = 3, but A has only one non-zero eigenvalue.
A matrix is said to have an eigenvalue if there is a scalar λ such that the determinant of the matrix minus λ times the identity matrix is zero. In other words, if A is a matrix and λ is an eigenvalue of A, then:
det(A - λI) = 0
where I is the identity matrix.
For a 3x3 matrix with every element being equal to 1, we can write:
A = [1 1 1; 1 1 1; 1 1 1]
To find the eigenvalues of A, we need to solve the equation:
det(A - λI) = 0
Expanding the determinant, we get:
(1-λ) [(1-λ)(1-λ) - 1] - (1-λ)[(1-λ)(1-λ) - 1] + (1-λ) [(1-λ)(1-λ) - 1] = 0
Simplifying the above equation, we get:
(1-λ)^2 (1-λ-3) = 0
The roots of the above equation are λ = 1 and λ = 3.
But we know that A has only one non-zero eigenvalue. Therefore, the only possible eigenvalue of A is λ = 3.
Hence, the correct answer is 3.
Summary:
- A matrix has an eigenvalue if there is a scalar λ such that det(A - λI) = 0.
- For a 3x3 matrix with every element being equal to 1, the only possible eigenvalue is 3.
- This is because the roots of the characteristic equation are λ = 1 and λ = 3, but A has only one non-zero eigenvalue.
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Consider 3*3 matrix with every element being equal to 1. Its only non-zero eigenvalue is _________Correct answer is '3'. Can you explain this answer?
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Consider 3*3 matrix with every element being equal to 1. Its only non-zero eigenvalue is _________Correct answer is '3'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Consider 3*3 matrix with every element being equal to 1. Its only non-zero eigenvalue is _________Correct answer is '3'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider 3*3 matrix with every element being equal to 1. Its only non-zero eigenvalue is _________Correct answer is '3'. Can you explain this answer?.
Consider 3*3 matrix with every element being equal to 1. Its only non-zero eigenvalue is _________Correct answer is '3'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Consider 3*3 matrix with every element being equal to 1. Its only non-zero eigenvalue is _________Correct answer is '3'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider 3*3 matrix with every element being equal to 1. Its only non-zero eigenvalue is _________Correct answer is '3'. Can you explain this answer?.
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