Which of the following matrices can NOT be obtained from the matr… - Vidyadip

MCQ

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?

A
$\left[\begin{array}{cc}0 & 1 \\ 1 & -1\end{array}\right]$
B
$\left[\begin{array}{cc}1 & -1 \\ -1 & 2\end{array}\right]$
✓
$\left[\begin{array}{ll}-1 & 2 \\ -2 & 7\end{array}\right]$
D
$\left[\begin{array}{ll}-1 & 2 \\ -1 & 3\end{array}\right]$

✓

Answer

Correct option: C.

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

c
$A=\left[\begin{array}{cc}-1 & 2 \\1 & -1\end{array}\right]$

$R _{1} \rightarrow R _{1}+ R _{2} ;\left[\begin{array}{cc}0 & 1 \\ 1 & -1\end{array}\right]$ possible

$R _{1} \leftrightarrow R _{2} ;\left[\begin{array}{cc}1 & -1 \\ -1 & 2\end{array}\right]$ possible

Option is not possible

$R _{2} \rightarrow R _{2}+2 R _{1} ;\left[\begin{array}{rr}-1 & 2 \\ -1 & 3\end{array}\right]$ possible

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