Answer
a. reduced echelon form
b. reduced echelon form
c. not in echelon form
c. echelon form, not reduced
Work Step by Step
a. There are no zero rows. The leading entry in each column is to the left of the leading entry of the previous column, all leading entries are 1, and the other entries in each column with a leading entry are all 0. The 1 in position (3,4) is not problematic, because it is not in a column with a leading entry.
b. There are no zero rows. The leading entry in each column is to the left of the leading entry of the previous column, all leading entries are 1, and the other entries in each column with a leading entry are all 0. Column (3) is not problematic, since this column contains no leading entries.
c. A row of all zeros occurs before a row with a nonzero entry, so the matrix is not in echelon form.
d. There are no zero rows. Beneath each leading entry, there are only zeros. There are nonzero entries above some leading entries, so the matrix is not in reduced echelon form. Note that column (3) is not problematic: columns of all zeros are allowed to occur in echelon form matrices.
