Question

If $\left|\begin{array}{ccc}a& 5x& p\\ b& 10y& 5\\ c& 15z& 15\end{array}\right|=125$, then find the value of $\left|\begin{array}{ccc}3a& 3b& c\\ x& 2y& z\\ p& 5& 5\end{array}\right|$

• A. 25
• B. 125
• C. 5
• D. 10

Answer 1

Answer: (A)

$\left|\begin{array}{ccc}3a& 3b& c\\ x& 2y& z\\ p& 5& 5\end{array}\right|=\left|\begin{array}{ccc}3a& x& p\\ 3b& 2y& 5\\ c& z& 5\end{array}\right|$ [changing rows intocolumns]
$=\frac{1}{3}\left|\begin{array}{ccc}3a& x& p\\ 3b& 2y& 5\\ 3c& 3z& 15\end{array}\right|=\frac{3}{3}\times \frac{1}{5}\left|\begin{array}{ccc}a& 5x& p\\ b& 10y& 5\\ c& 15z& 15\end{array}\right|=\frac{1}{5}\left(125\right)=25$