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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
If $A = \left( {\begin{array}{*{20}{c}}1&2&0\\0&1&2\\2&0&1\end{array}} \right),$then $adj \,A$
  • A
    $\left( {\begin{array}{*{20}{c}}1&4&{ - 2}\\{ - 2}&1&4\\4&{ - 2}&1\end{array}} \right)$
  • ✓
    $\left( {\begin{array}{*{20}{c}}1&{ - 2}&4\\4&1&{ - 2}\\{ - 2}&4&1\end{array}} \right)$
  • C
    $\left( {\begin{array}{*{20}{c}}1&2&4\\{ - 4}&1&2\\{ - 4}&{ - 2}&1\end{array}} \right)$
  • D
    None of these
✓

Answer

Correct option: B.
$\left( {\begin{array}{*{20}{c}}1&{ - 2}&4\\4&1&{ - 2}\\{ - 2}&4&1\end{array}} \right)$
b
(b) $A = \left[ {\begin{array}{*{20}{c}}1&2&0\\0&1&2\\2&0&1\end{array}} \right]$,

${A_{11}} = 1,\,{A_{21}} = - 2,\,{A_{31}} = 4$

${A_{12}} = 4,\,{A_{22}} = 1,\,{A_{32}} = - 2$

${A_{13}} = - 2,\,{A_{23}} = 4,\,{A_{33}} = 1$

$Adj\,(A) = \left[ {\begin{array}{*{20}{c}}1&{ - 2}&4\\4&1&{ - 2}\\{ - 2}&4&1\end{array}} \right]$.

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