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 find the reduced row-echelon form (RREF) of the given matrix, we perform a series of row operations to simplify the matrix as much as possible while maintaining its equivalence. The goal is to achieve a form where each leading entry of a row is 1, all entries in a column containing a leading 1 are zero except the leading 1 itself, and each leading 1 is to the right of the leading 1 in the row above it. The correct answer, option E, reflects these conditions after performing the necessary row operations on the given matrix.

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 $\left[ \begin{array} { r r r } 4 & 5 & 11 \\3 & 1 & - 11 \\3 & 5 & 17\end{array} \right]$