Question

Which of the following matrices can NOT be obtained from the matrix $\begin{bmatrix}-1 & 2 \\ 1 & -1\end{bmatrix}$ by a single elementary row operation?

• A. $\begin{bmatrix}0 & 1 \\ 1 & -1\end{bmatrix}$
• B. $\begin{bmatrix}1 & -1 \\ -1 & 2\end{bmatrix}$
• C. $\begin{bmatrix}-1 & 2 \\ -2 & 7\end{bmatrix}$
• D. $\begin{bmatrix}-1 & 2 \\ -1 & 3\end{bmatrix}$

Answer 1

Answer: (C)

$A=\begin{bmatrix}-1 & 2 \\1 & -1\end{bmatrix}$
(1) $R _1 \rightarrow R _1+ R _2 ;\begin{bmatrix}0 & 1 \\ 1 & -1\end{bmatrix}$ possible
(2) $R _1 \leftrightarrow R _2$; $\begin{bmatrix}1 & -1 \\ -1 & 2\end{bmatrix}$ possible
(3) Option is not possible
(4) $R_2 \rightarrow R_2+2 R_1$; $\begin{bmatrix}-1 & 2 \\ -1 & 3\end{bmatrix}$ possible