Determine whether the matrix is in echelon form, reduced echelon form, or neither.
-$$\left[ \begin{array} { r r r r }
1 & 6 & 2 & - 7 \
0 & 1 & - 4 & - 6 \
0 & 0 & 0 & 0
\end{array} \right]$$
A)Echelon form
B)Neither
C)Reduced echelon form

Question

Determine whether the matrix is in echelon form, reduced echelon form, or neither.
-$$\left[ \begin{array} { r r r r } 
1 & 6 & 2 & - 7 \
0 & 1 & - 4 & - 6 \
0 & 0 & 0 & 0
\end{array} \right]$$
A)Echelon form
B)Neither
C)Reduced echelon form

Quizplus · Accepted Answer

The matrix is in echelon form because each leading entry (first non-zero number from the left in a row) is to the right of the leading entry in the row above it, and rows with all zeros are at the bottom. It is not in reduced echelon form because not all leading entries are 1 (although they are in this case) and not every leading 1 has zeros above and below in its column.

Determine Whether the Matrix Is in Echelon Form, Reduced Echelon [162−701−4−60000]\left[ \begin{array} { r r r r } 1 & 6 & 2 & - 7 \\0 & 1 & - 4 & - 6 \\0 & 0 & 0 & 0\end{array} \right]​100​610​2−40​−7−60​​

Determine Whether the Matrix Is in Echelon Form, Reduced Echelon $\left[ \begin{array} { r r r r } 1 & 6 & 2 & - 7 \\0 & 1 & - 4 & - 6 \\0 & 0 & 0 & 0\end{array} \right]$