Which of the following matrices can NOT be ob | vedclass

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(C) Let $A = \left[\begin{array}{cc}-1 & 2 \ 1 & -1\end{array}ight]$.$1$. For option $A$: Applying $R_1 ightarrow R_1 + R_2$,we get $\left[\begin

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$\left[\begin{array}{cc}-1 & 2 \ -2 & 7\end{array}ight]$

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(C) Let $A = \left[\begin{array}{cc}-1 & 2 \ 1 & -1\end{array}ight]$.$1$. For option $A$: Applying $R_1 ightarrow R_1 + R_2$,we get $\left[\begin{array}{cc}-1+1 & 2-1 \ 1 & -1\end{array}ight] = \left[\begin{array}{cc}0 & 1 \ 1 & -1\end{array}ight]$. This is possible.$2$. For option $B$: Applying $R_1 \leftrightarrow R_2$,we get $\left[\begin{array}{cc}1 & -1 \ -1 & 2\end{array}ight]$. This is possible.$3$. For option $C$: To get $\left[\begin{array}{cc}-1 & 2 \ -2 & 7\end{array}ight]$,we would need $R_2 ightarrow R_2 + k R_1$. Here,$-1 + k(-1) = -2 \implies k=1$,but then $2 + k(2) = 2 + 1(2) = 4 
eq 7$. Thus,this is not possible.$4$. For option $D$: Applying $R_2 ightarrow R_2 + 2R_1$,we get $\left[\begin{array}{cc}-1 & 2 \ 1+2(-1) & -1+2(2)\end{array}ight] = \left[\begin{array}{cc}-1 & 2 \ -1 & 3\end{array}ight]$. This is possible.Therefore,the matrix in option $C$ cannot be obtained by a single elementary row operation.

Which of the following matrices can $NOT$ be obtained from the matrix $\left[\begin{array}{cc}-1 & 2 \\ 1 & -1\end{array}\right]$ by a single elementary row operation?

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