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Provide Solution For  R.D.Sharma Maths Class 12 Chapter determinants Exercise 5.2 Question 2 Sub Question 3 Maths Textbook Solution.

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Answer:\left|\begin{array}{ccc} 2 & 3 & 7 \\ 13 & 17 & 5 \\ 15 & 20 & 12 \end{array}\right|=0

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

Given:\left|\begin{array}{ccc} 2 & 3 & 7 \\ 13 & 17 & 5 \\ 15 & 20 & 12 \end{array}\right|

Solution:\left|\begin{array}{ccc} 2 & 3 & 7 \\ 13 & 17 & 5 \\ 15 & 20 & 12 \end{array}\right|

\begin{aligned} &\text { Applying } R_{1} \rightarrow R_{1}+R_{2} \\ &=\left|\begin{array}{ccc} 15 & 20 & 12 \\ 13 & 17 & 5 \\ 15 & 20 & 12 \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 R_{1}=R_{3}\right)

Hence,\left|\begin{array}{ccc} 2 & 3 & 7 \\ 13 & 17 & 5 \\ 15 & 20 & 12 \end{array}\right|=0

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