Answer
The matrix is in row-echelon form, but not reduced row-echelon form.
Work Step by Step
There are 3 main rules for a matrix to be in row echelon form:
1. A row of all 0s must be at the bottom.
2. The first non-zero entry in a row must be a 1. This is called the leading 1.
3. The leading 1 in a higher row must be in a column further to the left than a lower leading 1.
For a matrix to be in reduced row echelon form, the rules for row echelon form must be met with the addition of this rule:
4. Every column with a leading 1 must have all 0s above the leading 1.
Rules 1 - 3 are followed, so the matrix is in row-echelon form. However, rule 4 is not followed as the leading 1 in row 3 has non-zero numbers above it.
The matrix is in row-echelon form, but not reduced row-echelon form.
