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Thanu Dharshani posted an Question
July 13, 2021 • 00:22 am
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30 points
30 points
- IIT JAM
- Mathematics (MA)
Let n 2 2. which of the following statements is true for every n x n real matrix a of rank one? (a) there exist matrices p, qe m,(r) such that all the entries o
Let n 2 2. Which of the following statements is true for every n x n real matrix A of rank one? (a) There exist matrices P, QE M,(R) such that all the entries of the matrix PAQ are equal to 1. (b) There exists an invertible matrix P E M, (R) such that PAP-l is a diagonal matrix. (c) A has a nonzero eigenvalue. (d) The vector (1, 1,... , 1) E R" is an eigenvector for
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Alka gupta Best Answer
clearly here option B is correct if A has rank 1 for n greater than or equal to 2 then atleast one eigen value is zero then we have n LI Eigen vectors and we know that if matrix have n LI Eigen vectors then it is daigonalisable so options B is correct