Q98 / 150 · MHT CET 2021 (24 Sep Shift 1) · Mathematics

If $A=\left[\begin{array}{ccc}5 & 6 & 3 \\ -4 & 3 & 2 \\ -4 & -7 & 3\end{array}\right]$, then cofactors of all elements of second row are respectively.

  • A
    $-39,3,11$
  • Correct answer
    B
    $-39,27,11$
  • C
    $39,-3-11$
  • D
    $-39,-27,11$

Solution

$$ A=\left[\begin{array}{ccc} 5 & 6 & 3 \\ -4 & 3 & 2 \\ -4 & -7 & 3 \end{array}\right] $$ Cofactors of elements in second row are Cofactor of -4 Cofactor of 3 $$ \begin{aligned} & =(-1)^{2+1}\left|\begin{array}{cc} 6 & 3 \\ -7 & 3 \end{array}\right|=-(18+21)=-39 \\ & =(-1)^{2+2}\left|\begin{array}{cc} 5 & 3 \\ -4 & 3 \end{array}\right|=15+12=27 \\ & =(-1)^{2+3}\left|\begin{array}{cc} 5 & 6 \\ -4 & -7 \end{array}\right|=-(-35+24)=11 \end{aligned} $$

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

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