Write the matrix in reduced row-echelon form. $$\left[ \begin{array} { r r r }
4 & 5 & 11 \
3 & 1 & - 11 \
3 & 5 & 17
\end{array} \right]$$
A) $\left[ \begin{array} { r r r }
1 & 0 & - 6 \
0 & 0 & 0 \
0 & 0 & 0
\end{array} \right]$
B) $\left[ \begin{array} { l l l }
1 & 0 & 0 \
0 & 1 & 0 \
0 & 0 & 0
\end{array} \right]$
C) $\left[ \begin{array} { c c c }
1 & 0 & - 4 \
0 & 1 & 5 \
0 & 0 & 1
\end{array} \right]$
D) $\left[ \begin{array} { c c c }
1 & 0 & - 7 \
0 & 1 & - 6 \
0 & 0 & 0
\end{array} \right]$
E) $\left[ \begin{array} { r r r }
1 & 0 & - 6 \
0 & 1 & 7 \
0 & 0 & 0
\end{array} \right]$

Question

Write the matrix in reduced row-echelon form. $$\left[ \begin{array} { r r r } 
4 & 5 & 11 \
3 & 1 & - 11 \
3 & 5 & 17
\end{array} \right]$$
A) $\left[ \begin{array} { r r r } 
1 & 0 & - 6 \
0 & 0 & 0 \
0 & 0 & 0
\end{array} \right]$
B) $\left[ \begin{array} { l l l } 
1 & 0 & 0 \
0 & 1 & 0 \
0 & 0 & 0
\end{array} \right]$  
C) $\left[ \begin{array} { c c c } 
1 & 0 & - 4 \
0 & 1 & 5 \
0 & 0 & 1
\end{array} \right]$  
D) $\left[ \begin{array} { c c c } 
1 & 0 & - 7 \
0 & 1 & - 6 \
0 & 0 & 0
\end{array} \right]$  
E) $\left[ \begin{array} { r r r } 
1 & 0 & - 6 \
0 & 1 & 7 \
0 & 0 & 0
\end{array} \right]$

Quizplus · Accepted Answer

To convert the given matrix to reduced row-echelon form, we perform a series of row operations. The goal is to make the leading entry of each row a 1 (if it is not already) and to make all other entries in the column containing this leading 1 equal to 0. After performing these operations on the given matrix, we obtain the matrix in option E, which has leading 1s in the first two rows and zeros everywhere else in their columns, with the third row being all zeros, indicating that it is a dependent row. This process involves making the first entry of the first row a 1, using it to eliminate the first entry in the other rows, then making the second entry of the second row a 1 and using it to eliminate the second entry in the other rows, and finally observing that the third row can be reduced to all zeros due to dependency on the first two rows.

Write the Matrix in Reduced Row-Echelon Form [451131−113517]\left[ \begin{array} { r r r } 4 & 5 & 11 \\3 & 1 & - 11 \\3 & 5 & 17\end{array} \right]​433​515​11−1117​​

Write the Matrix in Reduced Row-Echelon Form $\left[ \begin{array} { r r r } 4 & 5 & 11 \\3 & 1 & - 11 \\3 & 5 & 17\end{array} \right]$