Q63 / 125 · BITSAT 2010 · Mathematics

The value of \(\left|\begin{array}{ccc}1 & 2 & 3 \\ -4 & 3 & 6 \\ 2 & -7 & 9\end{array}\right|\) is

  • A
    213
  • B
    -231
  • Correct answer
    C
    231
  • D
    39

Solution

\(\begin{aligned} & \left|\begin{array}{ccc}1 & 2 & 3 \\ -4 & 3 & 6 \\ 2 & -7 & 9\end{array}\right|=1\left|\begin{array}{cc}3 & 6 \\ -7 & 9\end{array}\right|-2\left|\begin{array}{cc}-4 & 6 \\ 2 & 9\end{array}\right|+3 \\ & \left|\begin{array}{cc}-4 & 3 \\ 2 & -7\end{array}\right| \\ & \end{aligned}\) \(\begin{aligned} & =1(3 \times 9-6(-7))-2(-4 \times 9-2 \times 6)+3 \\ & ((-4)(-7)-3 \times 2) \\ & =(27+42)-2(-36-12)+3(28-6)=231 \end{aligned}\)

Hence, the correct answer is option: 'C'.

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