Which of the following matrices can NOT be obtained from the matrix - 1 2 1 - 1 by a single elementary row…

Which of the following matrices can NOT be obtained from the matrix

[\begin{matrix} - 1 & 2 \\ 1 & - 1 \end{matrix}]

by a single elementary row operation?

$[\begin{matrix} 0 & 1 \\ 1 & - 1 \end{matrix}]$
$[\begin{matrix} 1 & - 1 \\ - 1 & 2 \end{matrix}]$
$[\begin{array}{l} - 1 & 2 \\ - 2 & 7 \end{array}]$
$[\begin{array}{r} - 1 & 2 \\ - 1 & 3 \end{array}]$

Solution

Given $A = [\begin{matrix} - 1 & 2 \\ 1 & - 1 \end{matrix}]$
(1) $R_{1} \to R_{1} + R_{2}$
$[\begin{matrix} 0 & 1 \\ 1 & - 1 \end{matrix}]$
(2) $R_{1} \leftrightarrow R_{2}$
$[\begin{matrix} 1 & - 1 \\ - 1 & 2 \end{matrix}]$
(3) Option is not possible
(4) $R_{2} \to R_{2} + 2 R_{1}$
$[\begin{matrix} - 1 & 2 \\ - 1 & 3 \end{matrix}]$

Asked in: JEE Main 2022 (29 Jul Shift 2)

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