Write the matrix in reduced row-echelon form. $$\left[ \begin{array} { r r r r }
9 & - 6 & - 3 & - 33 \
8 & - 1 & 1 & - 47 \
- 7 & - 7 & 6 & - 8
\end{array} \right]$$
A) $\left[ \begin{array} { l l l l }
1 & 0 & 0 & 0 \
0 & 1 & 0 & 0 \
0 & 0 & 1 & 0
\end{array} \right]$
B) $\left[ \begin{array} { l l l r }
1 & 0 & 0 & - 5 \
0 & 1 & 0 & - 6 \
0 & 0 & 1 & 1
\end{array} \right]$
C) $\left[ \begin{array} { r r r r }
1 & 0 & 0 & - 6 \
0 & 1 & 0 & 2 \
0 & 0 & 1 & - 6
\end{array} \right]$
D) $\left[ \begin{array} { r r r r }
1 & 0 & 0 & - 5 \
0 & 1 & 0 & 1 \
0 & 0 & 1 & - 6
\end{array} \right]$
E) $\left[ \begin{array} { l l l l }
1 & 0 & 0 & 1 \
0 & 1 & 0 & 1 \
0 & 0 & 1 & 1
\end{array} \right]$

Question

Write the matrix in reduced row-echelon form. $$\left[ \begin{array} { r r r r } 
9 & - 6 & - 3 & - 33 \
8 & - 1 & 1 & - 47 \
- 7 & - 7 & 6 & - 8
\end{array} \right]$$
A) $\left[ \begin{array} { l l l l } 
1 & 0 & 0 & 0 \
0 & 1 & 0 & 0 \
0 & 0 & 1 & 0
\end{array} \right]$  
B) $\left[ \begin{array} { l l l r } 
1 & 0 & 0 & - 5 \
0 & 1 & 0 & - 6 \
0 & 0 & 1 & 1
\end{array} \right]$  
C) $\left[ \begin{array} { r r r r } 
1 & 0 & 0 & - 6 \
0 & 1 & 0 & 2 \
0 & 0 & 1 & - 6
\end{array} \right]$  
D) $\left[ \begin{array} { r r r r } 
1 & 0 & 0 & - 5 \
0 & 1 & 0 & 1 \
0 & 0 & 1 & - 6
\end{array} \right]$  
E) $\left[ \begin{array} { l l l l } 
1 & 0 & 0 & 1 \
0 & 1 & 0 & 1 \
0 & 0 & 1 & 1
\end{array} \right]$

Quizplus · Accepted Answer

The matrix is row-reduced to have leading 1s in each row and zeros elsewhere, resulting in the reduced row-echelon form shown in option D.

Write the Matrix in Reduced Row-Echelon Form [9−6−3−338−11−47−7−76−8]\left[ \begin{array} { r r r r } 9 & - 6 & - 3 & - 33 \\8 & - 1 & 1 & - 47 \\- 7 & - 7 & 6 & - 8\end{array} \right]​98−7​−6−1−7​−316​−33−47−8​​

Write the Matrix in Reduced Row-Echelon Form $\left[ \begin{array} { r r r r } 9 & - 6 & - 3 & - 33 \\8 & - 1 & 1 & - 47 \\- 7 & - 7 & 6 & - 8\end{array} \right]$