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?

(C) $\left[\begin{array}{ll}-1 & 2 \\ -2 & 7\end{array}\right]$

(A) $\left[\begin{array}{cc}0 & 1 \\ 1 & -1\end{array}\right]$

(B) $\left[\begin{array}{cc}1 & -1 \\ -1 & 2\end{array}\right]$

(D) $\left[\begin{array}{ll}-1 & 2 \\ -1 & 3\end{array}\right]$

JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Matrices

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

[- 1 1 2 - 1]

by a single elementary row operation?

Answer: (C)

Starting with

A = [- 1 1 2 - 1]

, we check each option:
(A)

R_{1} \to R_{1} + R_{2}

gives

[01 1 - 1]

— possible.
(B)

R_{1} \leftrightarrow R_{2}

gives

[1 - 1 - 1 2]

— possible.
(C) No single elementary row operation produces

[- 1 - 2 27]

— not possible.
(D)

R_{2} \to R_{2} + 2 R_{1}

gives

[- 1 - 1 23]

— possible.

JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Single correct option