Q46 / 160 · TS EAMCET 2023 (14 May Shift 1) · Mathematics

If adj $\left[\begin{array}{ccc}1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1\end{array}\right]=\left[\begin{array}{ccc}5 & m & -2 \\ 1 & 1 & 0 \\ -2 & -2 & n\end{array}\right]$, then $m+n=$

  • A
    $2$
  • B
    $-3$
  • Correct answer
    C
    $5$
  • D
    $-5$

Solution

$\operatorname{adj}\left[\begin{array}{ccc}1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1\end{array}\right]$ $\begin{aligned} & \mathrm{C}_{11}=5, \mathrm{C}_{21}=4, \mathrm{C}_{31}=-2 \\ & \mathrm{C}_{12}=1, \mathrm{C}_{22}=1, \mathrm{C}_{32}=0 \\ & \mathrm{C}_{13}=-2, \mathrm{C}_{23}=-2, \mathrm{C}_{33}=1 \\ & \therefore \text { adj }\left[\begin{array}{ccc}1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1\end{array}\right]=\left[\begin{array}{ccc}5 & 4 & -2 \\ 1 & 1 & 0 \\ -2 & -2 & 1\end{array}\right] \\ & m=4, n=1 \\ & \therefore m+n=5\end{aligned}$

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

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