Provide Solution For  R.D. Sharma Maths Class 12 Chapter determinants Exercise 5.2 Question 2 Sub Question 9 Maths Textbook Solution.

Answer:$\left|\begin{array}{lll} 1 & 43 & 6 \\ 7 & 35 & 4 \\ 3 & 17 & 2 \end{array}\right|=0$

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

Given:$\left|\begin{array}{lll} 1 & 43 & 6 \\ 7 & 35 & 4 \\ 3 & 17 & 2 \end{array}\right|$

Solution:$\left|\begin{array}{lll} 1 & 43 & 6 \\ 7 & 35 & 4 \\ 3 & 17 & 2 \end{array}\right|$

\begin{aligned} &\text { Applying } C_{3} \rightarrow 7 \times C_{3}+C_{1} \\ &=\left|\begin{array}{lll} 1 & 43 & 6 \times 7+1 \\ 7 & 35 & 4 \times 7+7 \\ 3 & 17 & 2 \times 7+3 \end{array}\right| \\ &=\left|\begin{array}{lll} 1 & 43 & 42+1 \\ 7 & 35 & 28+7 \\ 3 & 17 & 14+3 \end{array}\right| \\ &=\left|\begin{array}{lll} 1 & 43 & 43 \\ 7 & 35 & 35 \\ 3 & 17 & 17 \end{array}\right| \end{aligned}

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

The value of the determinant is zero

$=0 \quad\left(\because C_{2}=C_{3}\right)$

Hence $\left|\begin{array}{lll} 1 & 43 & 6 \\ 7 & 35 & 4 \\ 3 & 17 & 2 \end{array}\right|=0$