Let A be a 3 × 3 matrix of non-negative real numbers such that A [ 2 2 2 ] = 4 [ 1 1 1 ] then ( det A ) max is

Question

Let $A$ be a $3 \times 3$ matrix of non-negative real numbers such that $A$ $[\begin{matrix} 2 \\ 2 \\ 2 \end{matrix}]$ $= 4$ $[\begin{matrix} 1 \\ 1 \\ 1 \end{matrix}]$ then ${(\det A)}_{\max}$ is

Smart Achievers · Accepted Answer

(2)

$a_{1} + a_{2} + a_{3} = 2,$ $b_{1} + b_{2} + b_{3} = 2,$ $c_{1} + c_{2} + c_{3} = 2$

$(\det A) is maximum when a_{1} = 2,$ $b_{2} = 2,$ $c_{3} = 2 and all others are 0 .$

Solution

Q.
Let $A$ be a $3 \times 3$ matrix of non-negative real numbers such that $A$ $[\begin{matrix} 2 \\ 2 \\ 2 \end{matrix}]$ $= 4$ $[\begin{matrix} 1 \\ 1 \\ 1 \end{matrix}]$ then ${(\det A)}_{\max}$ is

1 12

2 8

3 16

4 32

Ans.
(2)

$a_{1} + a_{2} + a_{3} = 2,$ $b_{1} + b_{2} + b_{3} = 2,$ $c_{1} + c_{2} + c_{3} = 2$

$(\det A) is maximum when a_{1} = 2,$ $b_{2} = 2,$ $c_{3} = 2 and all others are 0 .$

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