Let M = ( a ij ), i , j ∈ 1, 2, 3 , be the 3 × 3 matrix such that a ij = 1 if j + 1 is…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
Let M = (aij ), i, j ∈ {1, 2, 3}, be the 3 × 3 matrix such that aij = 1 if j + 1 is divisible by i, otherwise
aij = 0 . Then which of the following statements is(are) true?
aij = 0 . Then which of the following statements is(are) true?
- M is invertible
- There exists a nonzero column matrix
such that 
- The set {X ∈
3 : MX = O} ≠ {0}, where O = 
- The matrix (M – 2I) is invertible, where I is the
3 × 3 identity matrix
Answer
(C) The set X ∈ 3 : MX = O ≠ 0 , where O =
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