Answer
(a) row-echelon (b) reduced row-echelon (c) neither
Work Step by Step
Based on the definitions and conditions of row-echelon and reduced row-echelon (section 10.3):
(a) This matrix is in a row-echelon form because all the leading entries are $1$'s, the leading entry of the second row is to the right of the leading entry above it, and the number below the leading entry of the first row is zero. However, it is not a reduced row-echelon because the number above the lead entry of the second row is $2$ not zero.
(b) This matrix is in a reduced row-echelon form because if satisfy the conditions of a row-echelon, plus the number above the leading entry of the second row is zero.
(c) the matrix is neither in a row-echelon form or a reduced row-echelon form because the leading entry of the third row is to the left of the leading entry of the second row.
