If = | , * 20 c x&y&z &q&r &b&c , |, then | , * 20 c x& 2y &z 2p … - Vidyadip

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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