JEE MAIN - Mathematics (2022 - 29th July Evening Shift - No. 2)

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 ?
$$\left[\begin{array}{cc}0 & 1 \\ 1 & -1\end{array}\right]$$
$$\left[\begin{array}{cc}1 & -1 \\ -1 & 2\end{array}\right]$$
$$\left[\begin{array}{rr}-1 & 2 \\ -2 & 7\end{array}\right]$$
$$\left[\begin{array}{ll}-1 & 2 \\ -1 & 3\end{array}\right]$$

Explanation

Given matrix $$A = \left[ {\matrix{ { - 1} & 2 \cr 1 & { - 1} \cr } } \right]$$

For option A :

$${R_1} \to {R_1} + {R_2}$$

$$A = \left[ {\matrix{ 0 & 1 \cr 1 & { - 1} \cr } } \right]$$

$$\therefore$$ Option A can be obtained.

For option B :

$${R_1} \leftrightarrow {R_2}$$

$$A = \left[ {\matrix{ 1 & { - 1} \cr { - 1} & 2 \cr } } \right]$$

$$\therefore$$ Option B can be obtained.

Option C :

Not possible by a single elementary row operation.

Option D :

$${R_2} \to {R_2} + 2{R_1}$$

$$A = \left[ {\matrix{ { - 1} & 2 \cr { - 1} & 3 \cr } } \right]$$

$$\therefore$$ Option D can be obtained.

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