#### explain solution RD Sharma class 12 chapter 5 Determinants exercise Fill in the blanks question 16 maths

Hint: Here, we use basic concept of determinant of matrix.

Given: $\Delta=\left[\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 x & 6 x & 9 x \end{array}\right]$

Solution:

$\Delta=\left[\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 x & 6 x & 9 x \end{array}\right]$

\begin{aligned} &=1\left[\begin{array}{cc} 5 & 6 \\ 6 x & 9 x \end{array}\right]-2\left[\begin{array}{cc} 4 & 6 \\ 3 x & 9 x \end{array}\right]+3\left[\begin{array}{cc} 4 & 5 \\ 3 x & 6 x \end{array}\right] \\ &=1(45 x-36 x)-2(36 x-18 x)+3(24 x-15 x) \\ &=9 x-36 x+27 x \\ &=0 \end{aligned}