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

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

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Answer:\left|\begin{array}{ccc} 1 & 3 & 5 \\ 2 & 6 & 10 \\ 31 & 11 & 38 \end{array}\right|=0

Hint: We will solve the determinant with respect to row one.

Given:\left|\begin{array}{ccc} 1 & 3 & 5 \\ 2 & 6 & 10 \\ 31 & 11 & 38 \end{array}\right|

Solution:\left|\begin{array}{ccc} 1 & 3 & 5 \\ 2 & 6 & 10 \\ 31 & 11 & 38 \end{array}\right|

\begin{aligned} &=1\left|\begin{array}{ll} 6 & 10 \\ 11 & 38 \end{array}\right|-3\left|\begin{array}{cc} 2 & 10 \\ 31 & 38 \end{array}\right|+5\left|\begin{array}{cc} 2 & 6 \\ 31 & 11 \end{array}\right| \\ &=1(6 \times 38-10 \times 11)-3(2 \times 38-10 \times 31)+5(2 \times 11-6 \times 31) \\ &=(228-110)-3(76-310)+5(22-186) \\ &=118-3(-234)+5(-164) \\ &=118+702-820 \\ &=820-820 \\ &=0 \end{aligned}

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