#### Please Solve R. D. Sharma class 12 Chapter determinants Exercise 5.2 Question 2 Sub Question 2 Maths textbook Solution.

Answer:$\left|\begin{array}{ccc} 6 & -3 & 2 \\ 2 & -1 & 2 \\ -10 & 5 & 2 \end{array}\right|=0$

Hint: We will try to do any two column or row equal

Given:$\left|\begin{array}{ccc} 6 & -3 & 2 \\ 2 & -1 & 2 \\ -10 & 5 & 2 \end{array}\right|$

Solution:$\left|\begin{array}{ccc} 6 & -3 & 2 \\ 2 & -1 & 2 \\ -10 & 5 & 2 \end{array}\right|$

\begin{aligned} &\text { On taking }(-2) \text { common from } \mathrm{C}_{1}\\ &=(-2)\left|\begin{array}{ccc} -3 & -3 & 2 \\ -1 & -1 & 2 \\ 5 & 5 & 2 \end{array}\right| \end{aligned}

If any two rows or columns of a determinant are identical.

The value of the determinant is zero

\begin{aligned} &=(-2) \times 0 \quad\left(\because C_{1}=C_{2}\right) \\ &=0 \end{aligned}

Hence $\left|\begin{array}{ccc} 6 & -3 & 2 \\ 2 & -1 & 2 \\ -10 & 5 & 2 \end{array}\right|=0$