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# On using elementary row operations $R_2\times R_1-3R_2$ in the following matrix equation $\begin{bmatrix}4 & 2\\3 & 3\end{bmatrix}=\begin{bmatrix}1 & 2\\0 & 3\end{bmatrix}\begin{bmatrix}2 & 0\\1 & 1\end{bmatrix}$,we have:

\begin{array}{1 1}(A)\quad\begin{bmatrix}5 & 7\\3 & 3\end{bmatrix}=\begin{bmatrix}1 & 7\\0 & 3\end{bmatrix}\begin{bmatrix}2 & 0\\1 & 1\end{bmatrix}\\(B)\quad\begin{bmatrix}5 & 7\\3 & 3\end{bmatrix}=\begin{bmatrix}1 & 2\\0 & 3\end{bmatrix}\begin{bmatrix}1 & 3\\1 & 1\end{bmatrix}\\(C)\quad\begin{bmatrix}5 & 7\\3 & 3\end{bmatrix}=\begin{bmatrix}1 & 2\\1 & 7\end{bmatrix}\begin{bmatrix}2 & 0\\1 & 1\end{bmatrix}\\(D)\quad\begin{bmatrix}4 & 2\\5 & 7\end{bmatrix}=\begin{bmatrix}1 & 2\\-3 & -3\end{bmatrix}\begin{bmatrix}2 & 0\\1 & 1\end{bmatrix}\end{array}

On using elementary row operation $R_1\rightarrow R_1-3R_2$ in the following matrix equation:

$\begin{bmatrix}4 & 2\\3 & 3\end{bmatrix}=\begin{bmatrix}1 & 2\\0 & 3\end{bmatrix}\begin{bmatrix}2 & 0\\1 & 0\end{bmatrix}$ We have,

Apply $R_1\rightarrow R_1-3R_2$

$\begin{bmatrix}-5 & -7\\3 & 3\end{bmatrix}=\begin{bmatrix}1 & -7\\0 & 3\end{bmatrix}\begin{bmatrix}-1 & -3\\1 & 1\end{bmatrix}$

question has been given as     R2 x R1 - 3R2