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  • Please Solve R. D. Sharma class 12 Chapter determinants Exercise 5.2 Question 1 sub question 8 Maths textbook Solution.

Please Solve R. D. Sharma class 12 Chapter  determinants Exercise 5.2 Question 1 Sub Question 8 Maths textbook Solution.

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Answer:\left|\begin{array}{ccc} 102 & 18 & 36 \\ 1 & 3 & 4 \\ 17 & 3 & 6 \end{array}\right|=0

Hint: We will solve the determinant w.r.t R_{1}

Given: \left|\begin{array}{ccc} 102 & 18 & 36 \\ 1 & 3 & 4 \\ 17 & 3 & 6 \end{array}\right|

Solution: \left|\begin{array}{ccc} 102 & 18 & 36 \\ 1 & 3 & 4 \\ 17 & 3 & 6 \end{array}\right|

\begin{aligned} &=102\left|\begin{array}{ll} 3 & 4 \\ 3 & 6 \end{array}\right|-18\left|\begin{array}{cc} 1 & 4 \\ 17 & 6 \end{array}\right|+36\left|\begin{array}{cc} 1 & 3 \\ 17 & 3 \end{array}\right| \\ &=102(6 \times 3-3 \times 4)-18(6 \times 1-4 \times 17)+36(1 \times 3-17 \times 3) \\ &=102(18-12)-18(6-68)+36(3-51) \\ &=102(6)-18(-62)+36(-48) \\ &=612+1116-1728 \\ &=1728-1728 \\ &=0 \end{aligned}

Hence \left|\begin{array}{ccc} 102 & 18 & 36 \\ 1 & 3 & 4 \\ 17 & 3 & 6 \end{array}\right|=0

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