Which of the following matrices can NOT be obtained from the matrix [ cases - 1 & 2 1 & - 1 cases ] by a single elementary row operation?

Correct answer: C. [ cases - 1 & 2 - 2 & 7 cases ] Given A = [ cases - 1 & 2 1 & - 1 cases ] (1) R _ 1 → R _ 1 + R _ 2 [ cases 0 & 1 1 & - 1 cases ] (2) R _ 1 ↔ R _ 2 [ cases 1 & - 1 - 1 & 2 cases ] (3) Option is not possible (4) R _ 2 → R _ 2 + 2 R _ 1 [ cases - 1 & 2 - 1 & 3 cases ]

JEE Main 202229 JulyEvening Shift

Exam: JEE Main
Year: 2022
Date: 29 July
Shift: Evening Shift
Subject: Mathematics
Chapter: Matrices

JEE Main 2022 · 29 July · Evening Shift · Mathematics · Matrices

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

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

\left[

\begin{cases}- 1 & 2 \\ 1 & - 1\end{cases}

\right]

by a single elementary row operation?

Options

A $\left[$ \begin{cases}0 & 1 \\ 1 & - 1\end{cases} $\right]$
B $\left[$ \begin{cases}1 & - 1 \\ - 1 & 2\end{cases} $\right]$
C $\left[$ \begin{cases}- 1 & 2 \\ - 2 & 7\end{cases} $\right]$
D $\left[$ \begin{cases}- 1 & 2 \\ - 1 & 3\end{cases} $\right]$

Correct answer

C. $\left[$ \begin{cases}- 1 & 2 \\ - 2 & 7\end{cases} $\right]$

Step-by-step solution

Given A = $\left[$ \begin{cases}- 1 & 2 \\ 1 & - 1\end{cases} $\right]$
(1) ${R}_{1} \to {R}_{1} + {R}_{2}$
\left[ $\begin{cases}0 & 1 \\ 1 & - 1\end{cases}$ \right] $</p><p>(2)$ {R}_{1} ↔ {R}_{2} $</p><p>\left[$ \begin{cases}1 & - 1 \\ - 1 & 2\end{cases} $\right]$
(3) Option is not possible
(4) ${R}_{2} \to {R}_{2} + 2{R}_{1}$
\left[ $\begin{cases}- 1 & 2 \\ - 1 & 3\end{cases}$ \right]

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