Determine whether the matrix is in row-echelon form and/or in reduced row-echelon form. $$\left[ \begin{array} { l l l l }
1 & 0 & 5 & 9 \
0 & 1 & 0 & 6 \
0 & 0 & 1 & 0
\end{array} \right]$$
A)The matrix is in reduced row-echelon form.
B)The matrix is not in row-echelon form but is in reduced row-echelon form.
C)The matrix is in row-echelon form but not in reduced row-echelon form.
D)The matrix is not in row-echelon or in reduced-row echelon form.

Question

Determine whether the matrix is in row-echelon form and/or in reduced row-echelon form. $$\left[ \begin{array} { l l l l } 
1 & 0 & 5 & 9 \
0 & 1 & 0 & 6 \
0 & 0 & 1 & 0
\end{array} \right]$$
A)The matrix is in reduced row-echelon form.
B)The matrix is not in row-echelon form but is in reduced row-echelon form.
C)The matrix is in row-echelon form but not in reduced row-echelon form.
D)The matrix is not in row-echelon or in reduced-row echelon form.

Quizplus · Accepted Answer

The matrix is in row-echelon form because each leading entry is to the right of the leading entry in the previous row and all entries below the leading entries are zero. However, it is not in reduced row-echelon form because not all leading entries are 1 (which they are in this case) and not all leading 1s have zeros above them in their column (the 5 in the third column violates this condition).

Determine Whether the Matrix Is in Row-Echelon Form And/or in Reduced