Use elementary row operations to write the matrix below in row echelon form. $$\left[ \begin{array} { c c c c }
1 & 2 & 1 & - 9 \
3 & 2 & 3 & - 27 \
2 & 0 & 4 & - 26
\end{array} \right]$$
A) $\left[ \begin{array} { c c c c }
1 & - 4 & - 5 & 0 \
0 & 1 & 4 & - 1 \
0 & 0 & 1 & 1
\end{array} \right]$
B) $\left[ \begin{array} { c c c c }
1 & 2 & 1 & - 9 \
0 & 1 & - 1 & 4 \
0 & 0 & 1 & - 4
\end{array} \right]$
C) $\left[ \begin{array} { c c c c }
1 & - 4 & 0 & - 5 \
0 & 1 & 4 & - 1 \
0 & 0 & 1 & 1
\end{array} \right]$
D) $\left[ \begin{array} { c c c c }
1 & - 4 & - 5 & 0 \
0 & 1 & - 1 & 4 \
0 & 0 & 1 & 1
\end{array} \right]$
E) $\left[ \begin{array} { l l l l }
1 & 2 & 1 & - 9 \
0 & 1 & 4 & - 1 \
0 & 0 & 1 & - 4
\end{array} \right]$

Question

Use elementary row operations to write the matrix below in row echelon form. $$\left[ \begin{array} { c c c c } 
1 & 2 & 1 & - 9 \
3 & 2 & 3 & - 27 \
2 & 0 & 4 & - 26
\end{array} \right]$$
A) $\left[ \begin{array} { c c c c } 
1 & - 4 & - 5 & 0 \
0 & 1 & 4 & - 1 \
0 & 0 & 1 & 1
\end{array} \right]$
B) $\left[ \begin{array} { c c c c } 
1 & 2 & 1 & - 9 \
0 & 1 & - 1 & 4 \
0 & 0 & 1 & - 4
\end{array} \right]$
C) $\left[ \begin{array} { c c c c } 
1 & - 4 & 0 & - 5 \
0 & 1 & 4 & - 1 \
0 & 0 & 1 & 1
\end{array} \right]$
D) $\left[ \begin{array} { c c c c } 
1 & - 4 & - 5 & 0 \
0 & 1 & - 1 & 4 \
0 & 0 & 1 & 1
\end{array} \right]$
E) $\left[ \begin{array} { l l l l } 
1 & 2 & 1 & - 9 \
0 & 1 & 4 & - 1 \
0 & 0 & 1 & - 4
\end{array} \right]$

Quizplus · Accepted Answer

To achieve row echelon form, we start with the given matrix and apply elementary row operations. The goal is to have leading 1s in each row, with zeros below each leading 1, and each leading 1 should be to the right of the leading 1 in the row above. Starting with the given matrix, we can subtract multiples of the first row from the other rows to create zeros below the leading 1 in the first column. Then, we can scale the second row to have a leading 1 and eliminate the entry below it. Finally, we scale the third row to have a leading 1. The correct transformation that follows these steps is represented by option B.

Use Elementary Row Operations to Write the Matrix Below in Row