Question

Using the symbols 1, 0, and *, enumerate all 3 x 3 RREF matrices.

Answer 1

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. 1 0 0
2. 0 1 0
3. 0 0 1
4. 1 1 0
5. 1 0 1
6. 0 1 1
7. 1 1 1