Question

If $\Delta = \left| \begin{matrix} x & y & z \\ p & q & r \\ a & b & c \end{matrix} \right|,$ then $\left| \begin{matrix} x & 2y & z \\ 2p & 4q & 2r \\ a & 2b & c \end{matrix} \right|$equals.

• A. $\Delta^{2}$
• B. $4\Delta$
• C. $3\Delta$
• D. None of these

Answer 1

Answer: (B)

$4\Delta$

Answer 2

Let $\Delta_{1} = \left| \begin{matrix} x & 2y & z \\ 2p & 4q & 2r \\ a & 2b & c \end{matrix} \right|$=$4\left| \begin{matrix} x & y & z \\ p & q & r \\ a & b & c \end{matrix} \right| = 4\Delta$.

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