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 ?
Solution
<p>Given matrix $A = \left[ {\matrix{
{ - 1} & 2 \cr
1 & { - 1} \cr
} } \right]$</p>
<p>For option A :</p>
<p>${R_1} \to {R_1} + {R_2}$</p>
<p>$A = \left[ {\matrix{
0 & 1 \cr
1 & { - 1} \cr
} } \right]$</p>
<p>$\therefore$ Option A can be obtained.</p>
<p>For option B :</p>
<p>${R_1} \leftrightarrow {R_2}$</p>
<p>$A = \left[ {\matrix{
1 & { - 1} \cr
{ - 1} & 2 \cr
} } \right]$</p>
<p>$\therefore$ Option B can be obtained.</p>
<p>Option C :</p>
<p>Not possible by a single elementary row operation.</p>
<p>Option D :</p>
<p>${R_2} \to {R_2} + 2{R_1}$</p>
<p>$A = \left[ {\matrix{
{ - 1} & 2 \cr
{ - 1} & 3 \cr
} } \right]$</p>
<p>$\therefore$ Option D can be obtained.</p>
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
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