JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) be a \(3 \times 3\) matrix of non-negative real elements such that \(A\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]=3\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]\). Then the maximum value of \(\operatorname{det}(\mathrm{A})\) is ...........
- A \(49\)
- B \(54\)
- C \(27\)
- D \(50\)
Answer & Solution
Correct Answer
(C) \(27\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \text { Let } A & =\left[\begin{array}{lll}a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3\end{array}\right] \\ A\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right] & =3\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]\end{aligned}\)…
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