Consider a matrixPwhose only eigenvectors are the multiples of. Consider the following statements. (I)Pdoes not have an inverse (II)Phas a repeated eigenvalue (III)Pcannot be diagonalized Which one of the following options is correct?a)Only I and III are necessarily trueb)Only II is necessarily truec)Only I and II are necessarily trued)Only II and III are necessarily trueCorrect answer is option 'D'. Can you explain this answer? - EduRev Computer Science Engineering (CSE) Question

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Consider a matrix P whose only eigenvectors are the multiples of

. Consider the following statements. (I) P does not have an inverse (II) P has a repeated eigenvalue (III) P cannot be diagonalized Which one of the following options is correct?

a)
Only I and III are necessarily true
b)
Only II is necessarily true
c)
Only I and II are necessarily true
d)
Only II and III are necessarily true

Correct answer is option 'D'. Can you explain this answer?

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Consider a matrixPwhose only eigenvectors are the multiples of. Consid...

Repeated eigenvectors come from repeated eigenvalues. Therefore, statement (I) may not be correct, take any Identity matrix which has same eigenvalues but determinant so inverse exists. A matrix with repeated eigenvalues can or can not be diagonalized, repeated eigenvalues are necessary but not sufficient for a matrix to not be diagonalizable. But if all eigenvalues are distinct then we can be sure to be able to diagonalize it. In other words: as soon as all eigenvalues are distinct then we can be sure to be able to diagonalize it. Therefore, only statements (II) and (III) are necessarily true.

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Consider a matrixPwhose only eigenvectors are the multiples of. Consider the following statements. (I)Pdoes not have an inverse (II)Phas a repeated eigenvalue (III)Pcannot be diagonalized Which one of the following options is correct?a)Only I and III are necessarily trueb)Only II is necessarily truec)Only I and II are necessarily trued)Only II and III are necessarily trueCorrect answer is option 'D'. Can you explain this answer?

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Consider a matrixPwhose only eigenvectors are the multiples of. Consider the following statements. (I)Pdoes not have an inverse (II)Phas a repeated eigenvalue (III)Pcannot be diagonalized Which one of the following options is correct?a)Only I and III are necessarily trueb)Only II is necessarily truec)Only I and II are necessarily trued)Only II and III are necessarily trueCorrect answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider a matrixPwhose only eigenvectors are the multiples of. Consider the following statements. (I)Pdoes not have an inverse (II)Phas a repeated eigenvalue (III)Pcannot be diagonalized Which one of the following options is correct?a)Only I and III are necessarily trueb)Only II is necessarily truec)Only I and II are necessarily trued)Only II and III are necessarily trueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a matrixPwhose only eigenvectors are the multiples of. Consider the following statements. (I)Pdoes not have an inverse (II)Phas a repeated eigenvalue (III)Pcannot be diagonalized Which one of the following options is correct?a)Only I and III are necessarily trueb)Only II is necessarily truec)Only I and II are necessarily trued)Only II and III are necessarily trueCorrect answer is option 'D'. Can you explain this answer?.

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