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BITSAT 2012
Exam
BITSAT
Year
2012
Subject
Mathematics
Chapter
Determinants

BITSAT 2012 · Mathematics · Determinants

The value of the determinant | array lll 265 & 240 & 219 240 & 225...

The value of the determinant \left|265240219240225198219198181\begin{array}{lll}265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181\end{array}$\right| is$

Options

  1. A1000
  2. B779
  3. C679
  4. D0

Correct answer

D. 0

Step-by-step solution

Applying C1−C2\mathrm{C}_{1}-\mathrm{C}_{2} and C2−C3,\mathrm{C}_{2}-\mathrm{C}_{3}, we get  Det. =∣252121915271982117181∣=∣4219−1227−7241711∣=[4219090−450−42∣[ByR2+3R1,R3−R1]=4(180−180)=0\begin{aligned} \text{ Det. } &=\left|\begin{array}{ccc} 25 & 21 & 219 \\ 15 & 27 & 198 \\ 21 & 17 & 181 \end{array}\right|=\left|\begin{array}{ccc} 4 & 21 & 9 \\ -12 & 27 & -72 \\ 4 & 17 & 11 \end{array}\right| \\ =&\left[\begin{array}{llc} 4 & 21 & 9 \\ 0 & 90 & -45 \\ 0 & -4 & 2 \end{array} \mid\left[\mathrm{By} \mathrm{R}_{2}+3 \mathrm{R}_{1}, \mathrm{R}_{3}-\mathrm{R}_{1}\right]\right.\\ =4(180-180)=0 \end{aligned}
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