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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 $\left[ {\begin{array}{*{20}{c}}1&2&3\\3&1&2\\2&3&1\end{array}} \right]\,\left[ \begin{array}{l}x\\y\\z\end{array} \right] = \left[ {\begin{array}{*{20}{c}}4&{ - 2}\\0&{ - 6}\\{ - 1}&2\end{array}} \right]\,\left[ \begin{array}{l}2\\1\end{array} \right]$, then $(x,y,z)$=
  • ✓
    $( - 4,\,2,\,2)$
  • B
    $(4,\, - 2,\, - 2)$
  • C
    $(4,\,2,\,2)$
  • D
    $( - 4,\, - 2,\, - 2)$
✓

Answer

Correct option: A.
$( - 4,\,2,\,2)$
a
(a) $\left[ {\begin{array}{*{20}{c}}1&2&3\\3&1&2\\2&3&1\end{array}} \right]\,\,\left[ \begin{array}{l}x\\y\\z\end{array} \right] = \left[ {\begin{array}{*{20}{c}}4\\0\\{ - 1}\end{array}\,\,\begin{array}{*{20}{c}}{ - 2}\\{ - 6}\\2\end{array}} \right]\,\left[ \begin{array}{l}2\\1\end{array} \right]\,$

$\begin{array}{l}\,\,\,\,\,\,\,\,\,\,\,\,\,x + 2y + 3z = 6\\\, \Rightarrow \,\,\,\,\,3x + y + 2z = - \,6\\\,{\rm{ }}2x + 3y + z = 0\end{array}$

On Simplification the above equation, we get the required result i.e.,

$x = - 4,\,y = 2,\,z = 2$.

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