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InterviewSolution
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What is the value of the determinant \(\left |\begin{array}{ccc} \rm x+2 & \rm x+3 & \rm x+5 \\ \rm x+4 &\rm x+6 &\rm x+9 \\ \rm x+8 &\rm x+11 &\rm x+15 \end{array}\right|\)1. x - 22. -23. x+24. 2 |
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Answer» Correct Answer - Option 2 : -2 Calculation: Let Δ = \(\left |\begin{array}{ccc} \rm x+2 & \rm x+3 & \rm x+5 \\ \rm x+4 &\rm x+6 &\rm x+9 \\ \rm x+8 &\rm x+11 &\rm x+15 \end{array}\right|\) \(\begin{aligned} \\ &\text { By applying } \rm C_{2} \rightarrow C_{2}-C_{1}, C_{3} \rightarrow C_{3}-C_{1}\\ &=\left|\begin{array}{ccc} \rm x+1 & 1 & 3 \\ \rm x+3 & 2 & 5 \\ \rm x+7 & 3 & 7 \end{array}\right|\\ & \end{aligned}\) \(\text { By applying } \rm R_{2} \rightarrow R_{2}-R_{1}, \text { and } R_{3} \rightarrow R_{3}-R_{2}\\ \) \(= \left|\begin{array}{ccc} \rm x+1 & 1 & 3 \\ 2 & 1 & 2 \\ 4 & 1 & 2 \end{array}\right|\) = (x + 1) (0) - 1 (4 - 8) + 3(2 - 4) = 4 - 6 = -2 Hence, option (2) is correct. |
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