Let x ∈ R and let P= [ array lll 1 & 1 & 1 0 & 2 & 2 0 & 0 & 3 array ], Q= [ array ccc 2…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
Let x ∈ R and let
\[P=\left[\begin{array}{lll} 1 & 1 & 1 \\ 0 & 2 & 2 \\ 0 & 0 & 3 \end{array}\right], Q=\left[\begin{array}{ccc} 2 & x & x \\ 0 & 4 & 0 \\ x & x & 6 \end{array}\right] \text { and } R=P Q P^{-1} .\]
Then which of the following options is/are correct?
\[P=\left[\begin{array}{lll} 1 & 1 & 1 \\ 0 & 2 & 2 \\ 0 & 0 & 3 \end{array}\right], Q=\left[\begin{array}{ccc} 2 & x & x \\ 0 & 4 & 0 \\ x & x & 6 \end{array}\right] \text { and } R=P Q P^{-1} .\]
Then which of the following options is/are correct?
- There exists a real number x such that PQ = QP
- For x = 1 there exists a unit vector
for which 
Answer
(D)
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