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STD 12 - 3 and 4 . determinant and metrices — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 3 and 4 . determinant and metrices1 Mark
MCQ
If $\Delta = \left| {\,\begin{array}{*{20}{c}}x&y&z\\p&q&r\\a&b&c\end{array}\,} \right|,$ then $\left| {\,\begin{array}{*{20}{c}}x&{2y}&z\\{2p}&{4q}&{2r}\\a&{2b}&c\end{array}\,} \right|$equals
  • A
    ${\Delta ^2}$
  • ✓
    $4\Delta $
  • C
    $3\Delta $
  • D
    None of these
✓

Answer

Correct option: B.
$4\Delta $
b
(b) Let ${\Delta _1} = \left| {\,\begin{array}{*{20}{c}}x&{2y}&z\\{2p}&{4q}&{2r}\\a&{2b}&c\end{array}\,} \right|$=$4\,\left| {\,\begin{array}{*{20}{c}}x&y&z\\p&q&r\\a&b&c\end{array}\,} \right| = 4\Delta $.

(Taking common $'2'$ from $II^{nd}$ row and $'2'$ from $II^{nd}$ column).

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