Question

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

• A. 25
• B. 125
• C. 5
• D. 10

Answer 1

Answer: (A)

25

Answer 2

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