Question

# Which of the following is the augmented matrix of the system of equations x+2y+z=-1 2x-y+3z=-4? 3x+y-z=-2 (A)$\begin{bmatrix}1 & 2 & 1 & -1\\2 & -1 & 3 & -4\\3 & 1 & -1 & -2\end{bmatrix}$(B)$\begin{bmatrix}1 & 2 & 1 & 1\\2 & -1 & 3 & 4\\3 & 1 & -1 & 2\end{bmatrix}$(C)$\begin{bmatrix}1 & 2 & 1 & 0\\2 & -1 & 3 & 0\\3 & 1 & -1 & 0\end{bmatrix}$(D)$\begin{bmatrix}1 & 2 & 1\\2 & -1 & 3\\3 & 1 & -1\end{bmatrix}$(E)$\begin{bmatrix}1 & 2 & -1\\2 & -1 & -3\\3 & 1 & 1\end{bmatrix}$

Solution

Verified
Step 1
1 of 2

From the given, the original matrix is the second matrix. Notice that $-2$ times $R_1$ added to $R_2$ is used since:

$\left[ \begin{array}{rrr} 1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9 \end{array} \right]$

$(-2)R_1+R_2\to \left[ \begin{array}{rrr} 1 & 2 & 3\\ -2(1)+4 & -2(2)+5 & -2(3)+6\\ 7 & 8 & 9 \end{array} \right] = \left[ \begin{array}{rrr} 1 & 2 & 3\\ 2 & 1 & 0\\ 7 & 8 & 9 \end{array} \right]$

So, the correct answer is choice $\textbf{\color{#c34632}(B).}$

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