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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 $A = dig(2, - 1,\,3),B = dig( - 1,\,3,\,2)$, then ${A^2}B = $
  • A
    $dig\ (5, 4, 11)$
  • ✓
    $dig\ (-4, 3, 18)$
  • C
    $dig\ (3, 1, 8 )$
  • D
    $B$
✓

Answer

Correct option: B.
$dig\ (-4, 3, 18)$
b
(b) ${A^2}B = (A.\,A)B = \left[ {\begin{array}{*{20}{c}}2&0&0\\0&{ - 1}&0\\0&0&3\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}2&0&0\\0&{ - 1}&0\\0&0&3\end{array}} \right].\,\left[ {\begin{array}{*{20}{c}}{ - 1}&0&0\\0&3&0\\0&0&2\end{array}} \right]$

$ = \left[ {\begin{array}{*{20}{c}}4&0&0\\0&1&0\\0&0&9\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}{ - 1}&0&0\\0&3&0\\0&0&2\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{ - 4}&0&0\\0&3&0\\0&0&{18}\end{array}} \right]$.

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