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JEE Main20244 Apr 2024Morning ShiftMathematicsMatricesActual

Let A be a 3 3 matrix of non-negative real elements such that A [ array l 1 1 1 array ]=3 [ array l 1 1 1 array ] . Then the maximum value of det ( A ) is ______

Correct answer

0

Step-by-step solution

aligned Let A & = [ array lll a₁ & a₂ & a₃ b₁ & b₂ & b₃ c₁ & c₂ & c₃ array ] A [ array l 1 1 1 array ] & =3 [ array l 1 1 1 array ] aligned a₁+a₂+a₃=3 ...(1) b₁+b₂+b₃=3 ...(2) c₁+ ca ₂+ c ₃=3 ...(3) Now, aligned & |A|= (a₁ b₂ c₃+a₂ b₃ c₁+a₃ b₁ c₂ ) & - (a₃ b₂ c₁+a₂ b₁ c₃+a₁ b₃ c₂ ) aligned From above in formation, clearly | A |_ =27 , when a₁=3, b₂=3, c₃=3

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