# Which of the following metrice can be obtained by elementary transformation of $\begin{bmatrix} 1 &2 \\ 3& 4 \end{bmatrix}$ ? Option 1) $\begin{bmatrix} 1 &3 \\ 3& 4 \end{bmatrix}$ Option 2) $\begin{bmatrix} 2 &2 \\ 3& 4 \end{bmatrix}$ Option 3) $\begin{bmatrix} 2 &3 \\ 3& 4 \end{bmatrix}$ Option 4) $\begin{bmatrix} 2 &1 \\ 3& 4 \end{bmatrix}$

V Vakul

As we have learnt,

Elementary row (column) transformation -

Adding to the elements of a row (column) , the corresponding elements of any other row (column) multiplied by any scalar k

- wherein

$\\R_{i}\rightarrow R_{i}+kR_{j}\\\ C_{i}\rightarrow C_{i}+kC_{j} \right )$

$A = \begin{bmatrix} 1 &2\\ 3& 4 \end{bmatrix}$

$R_1 \rightarrow R_1 + R_2\;\;\;\;\; \begin{bmatrix} 4 &6\\ 3& 4 \end{bmatrix}$

$R_1 \rightarrow\frac{R_1}{2}\;\;\;\;\; \begin{bmatrix} 2&3\\ 3& 4 \end{bmatrix}$

Option 1)

$\begin{bmatrix} 1 &3 \\ 3& 4 \end{bmatrix}$

Option 2)

$\begin{bmatrix} 2 &2 \\ 3& 4 \end{bmatrix}$

Option 3)

$\begin{bmatrix} 2 &3 \\ 3& 4 \end{bmatrix}$

Option 4)

$\begin{bmatrix} 2 &1 \\ 3& 4 \end{bmatrix}$

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