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  • The positive value of the determinant of the matrix , whose <img alt="\operatorname{Adj}(\opera

The positive value of the determinant of the matrix \mathrm{A}, whose
\operatorname{Adj}(\operatorname{Adj}(\mathrm{A}))=\left(\begin{array}{rrr} 14 & 28 & -14 \\ -14 & 14 & 28 \\ 28 & -14 & 14 \end{array}\right) is______________.

Option: 1

14


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{\left|A d_{j}(\operatorname{Adj}(A))\right|=|A|^{(n-1)^{2}}=|A|^{2^{2}}=|A|^{4} .}

\mathrm{|\operatorname{Adj}(\operatorname{Adj} A)|=14 \times 14 \times 14\left|\begin{array}{ccc} 1 & 2 & -1 \\ -1 & 1 & 2 \\ 2 & -1 & 1 \end{array}\right|}

\mathrm{\Rightarrow|A|^{4}=14 \times 14 \times 14 \times[1 \times 3-2 \times(-5)-1 \times(-1)]} \\

\mathrm{\Rightarrow|A|^{4}=14^{4} \Rightarrow|A|=\pm 14 }

\mathrm{+ve\: value =14.}

Hence answer is \mathrm{14.}

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chirag

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