Question

Assuming that you have been given the below augmented matrix obtained from an unknown matrix A using the following elementary row operations given in the reverse or backward sense. Meaning that you must work the elementary operation from the back to the top. Elementary operations used in the reverse sense are: $R_2 - 2R_1 \to R_2$ $xR_2 \to R_2$ $R_2 + R_1$ The augmented matrix after the operation is $\begin{bmatrix} 2 & 2 \ 0 & -4 \\end{bmatrix} \begin{bmatrix} y \ 3x - 2y \\end{bmatrix}$ In the case of infinitely many solutions then the initial augmented matrix corresponding to the system is given by $\begin{bmatrix} 4 & 2 & | & 6 \ 0 & 0 & | & 3x - 2y \\end{bmatrix}$ None of the given options $\begin{bmatrix} 4 & -2 & | & 6 \ 0 & 0 & | & 0 \\end{bmatrix}$ $\begin{bmatrix} -2 & 1 & | & 3 \ 4 & 2 & | & 6 \\end{bmatrix}$ $\begin{bmatrix} 4 & 2 & | & 3 \ 1 & -4 & | & 0 \\end{bmatrix}$ $\begin{bmatrix} -4 & 2 & | & 6 \ 0 & -4 & | & -12 \\end{bmatrix}$

          Assuming that you have been given the below augmented matrix obtained from an unknown matrix A using the following elementary row operations given in the reverse or backward sense. Meaning that you must work the elementary operation from the back to the top.
Elementary operations used in the reverse sense are:
$R_2 - 2R_1 \to R_2$
$xR_2 \to R_2$
$R_2 + R_1$
The augmented matrix after the operation is
$\begin{bmatrix} 2 & 2 \ 0 & -4 \\end{bmatrix} \begin{bmatrix} y \ 3x - 2y \\end{bmatrix}$
In the case of infinitely many solutions then the initial augmented matrix corresponding to the system is given by
$\begin{bmatrix} 4 & 2 & | & 6 \ 0 & 0 & | & 3x - 2y \\end{bmatrix}$
None of the given options
$\begin{bmatrix} 4 & -2 & | & 6 \ 0 & 0 & | & 0 \\end{bmatrix}$
$\begin{bmatrix} -2 & 1 & | & 3 \ 4 & 2 & | & 6 \\end{bmatrix}$
$\begin{bmatrix} 4 & 2 & | & 3 \ 1 & -4 & | & 0 \\end{bmatrix}$
$\begin{bmatrix} -4 & 2 & | & 6 \ 0 & -4 & | & -12 \\end{bmatrix}$

Assuming that you have been given the below augmented matrix obtained from an unknown matrix A using the following elementary row operations given in the reverse or backward sense. Meaning that you must work the elementary operation from the back to the top.
Elementary operations used in the reverse sense are:
R2 - 2R1 → R2
xR2 → R2
R2 + R1
The augmented matrix after the operation is
< b m a t r i x >

Added by Francisco Javier L.

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