Convert the matrix to row-echelon form. $\left[ \begin{array} { c c c c }
1 & - 3 & 2 & 3 \
- 2 & 9 & - 6 & - 6 \
- 1 & 6 & - 5 & 0
\end{array} \right]$
A) $\left[ \begin{array} { l l l l }
1 & 1 & 2 & - 2 \
0 & 1 & 0 & - 3 \
0 & 0 & 1 & - 3
\end{array} \right]$
B) $\left[ \begin{array} { c c c c }
1 & - 3 & 2 & 3 \
0 & 1 & 0 & - 2 \
0 & 0 & 1 & - 3
\end{array} \right]$
C) $\left[ \begin{array} { c c c c }
1 & 3 & - 3 & - 2 \
0 & 1 & 0 & - 1 \
0 & 0 & 1 & - 2
\end{array} \right]$
D) $\left[ \begin{array} { c c c c }
1 & 0 & 2 & 0 \
0 & 1 & - 2 & 0 \
0 & 0 & 1 & - 3
\end{array} \right]$
E) $\left[ \begin{array} { c c c c }
1 & 2 & 2 & 1 \
0 & 1 & 0 & 6 \
0 & 0 & 1 & - 3
\end{array} \right]$

Question

Convert the matrix to row-echelon form. $\left[ \begin{array} { c c c c } 
1 & - 3 & 2 & 3 \
- 2 & 9 & - 6 & - 6 \
- 1 & 6 & - 5 & 0
\end{array} \right]$
A) $\left[ \begin{array} { l l l l } 
1 & 1 & 2 & - 2 \
0 & 1 & 0 & - 3 \
0 & 0 & 1 & - 3
\end{array} \right]$
B) $\left[ \begin{array} { c c c c } 
1 & - 3 & 2 & 3 \
0 & 1 & 0 & - 2 \
0 & 0 & 1 & - 3
\end{array} \right]$
C) $\left[ \begin{array} { c c c c } 
1 & 3 & - 3 & - 2 \
0 & 1 & 0 & - 1 \
0 & 0 & 1 & - 2
\end{array} \right]$
D) $\left[ \begin{array} { c c c c } 
1 & 0 & 2 & 0 \
0 & 1 & - 2 & 0 \
0 & 0 & 1 & - 3
\end{array} \right]$
E) $\left[ \begin{array} { c c c c } 
1 & 2 & 2 & 1 \
0 & 1 & 0 & 6 \
0 & 0 & 1 & - 3
\end{array} \right]$

Quizplus · Accepted Answer

Using elementary row operations, we can perform the following steps:
- Add 2 times the first row to the second row
- Add 1 times the first row to the third row
- Add 3 times the second row to the third row
This gives us the matrix in the row-echelon form: 
$$\left[\begin{array}{cccc}1 & -3 & 2 & 3\0 & 1 & 0 & -2\0 & 0 & 1 & -3\end{array}\right]$$

Convert the Matrix to Row-Echelon Form [1−323−29−6−6−16−50]\left[ \begin{array} { c c c c } 1 & - 3 & 2 & 3 \\- 2 & 9 & - 6 & - 6 \\- 1 & 6 & - 5 & 0\end{array} \right]​1−2−1​−396​2−6−5​3−60​​

Convert the Matrix to Row-Echelon Form $\left[ \begin{array} { c c c c } 1 & - 3 & 2 & 3 \\- 2 & 9 & - 6 & - 6 \\- 1 & 6 & - 5 & 0\end{array} \right]$