Final answer:
In a 3 x 3 RREF matrix, the first non-zero entry in each row must be 1 and each pivot must be the only non-zero entry in its column. All possible 3 x 3 RREF matrices using the symbols 1, 0, and * are listed.
Step-by-step explanation:
RREF stands for Row Reduced Echelon Form, which is a special form of a matrix obtained through row operations. In a 3 x 3 RREF matrix, the first non-zero entry in each row, called a pivot, must be 1. Additionally, each pivot must be the only non-zero entry in its column.
Using the symbols 1, 0, and *, we can construct all possible 3 x 3 RREF matrices:
- 1 0 0
- 0 1 0
- 0 0 1
- 1 1 0
- 1 0 1
- 0 1 1
- 1 1 1