माना $X =\left[x_{i j}\right]$ एक आव्यूह है, जहाँ $X=\left[\begin{array}{ccc}1 & -1 & 2 \\ 3 & 4 & -5 \\ 2 & -1 & 3\end{array}\right]$ तब आव्यूह $Y =\left[m_{i j}\right]$, जहाँ $m_{i j}=x_{i j}$ का उपसारिणक है-
CBSE 2021 (Term I)
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$(D) \left[\begin{array}{ccc}7 & 19 & -11 \\ -1 & -1 & 1 \\ -3 & -11 & 7\end{array}\right]$
यहाँ $X =\left[\begin{array}{ccc}1 & -1 & 2 \\ 3 & 4 & -5 \\ 2 & -1 & 3\end{array}\right]$
$\begin{aligned} \therefore m_{11} & =\left|\begin{array}{cc}4 & -5 \\ -1 & 3\end{array}\right|=12-5=7 \\ m_{12} & =\left|\begin{array}{cc}3 & -5 \\ 2 & 3\end{array}\right|=9+10=19 \\ m_{13} & =\left|\begin{array}{cc}3 & 4 \\ 2 & -1\end{array}\right|=-3-8=-11\end{aligned}$
इसी प्रकार,
$m_{21}=-1, m_{22}=-1, m_{23}=1$
$m_{31}=-3, m_{32}=-11, m_{33}=7$
$Y =\left[m_{i j}\right]=\left[\begin{array}{lll}m_{11} & m_{12} & m_{13} \\ m_{21} & m_{22} & m_{23} \\ m_{31} & m_{32} & m_{33}\end{array}\right]=\left[\begin{array}{ccc}7 & 19 & -11 \\ -1 & -1 & 1 \\ -3 & -11 & 7\end{array}\right]$
यहाँ $X =\left[\begin{array}{ccc}1 & -1 & 2 \\ 3 & 4 & -5 \\ 2 & -1 & 3\end{array}\right]$
$\begin{aligned} \therefore m_{11} & =\left|\begin{array}{cc}4 & -5 \\ -1 & 3\end{array}\right|=12-5=7 \\ m_{12} & =\left|\begin{array}{cc}3 & -5 \\ 2 & 3\end{array}\right|=9+10=19 \\ m_{13} & =\left|\begin{array}{cc}3 & 4 \\ 2 & -1\end{array}\right|=-3-8=-11\end{aligned}$
इसी प्रकार,
$m_{21}=-1, m_{22}=-1, m_{23}=1$
$m_{31}=-3, m_{32}=-11, m_{33}=7$
$Y =\left[m_{i j}\right]=\left[\begin{array}{lll}m_{11} & m_{12} & m_{13} \\ m_{21} & m_{22} & m_{23} \\ m_{31} & m_{32} & m_{33}\end{array}\right]=\left[\begin{array}{ccc}7 & 19 & -11 \\ -1 & -1 & 1 \\ -3 & -11 & 7\end{array}\right]$
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