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The question asks which of the given matrices is in **Reduced Row Echelon Form (RREF)**. 

To determine whether a matrix is in RREF, it must satisfy the following conditions:

1. **Leading 1s**: In each row, the first non-zero element (called the leading entry) is a 1.
2. **Zeroes above and below leading 1s**: Each leading 1 must be the only non-zero entry in its column.
3. **Row ordering**: The row with the leading 1 must be to the right of the leading 1 in the previous row.
4. **Zero rows**: Any row that consists entirely of zeroes should be at the bottom.

### Let's check each matrix for these criteria:

- **Matrix A**:  
  - The first row is \( [1 \ 0 \ 0 \ 3] \), with a leading 1 in the first position. However, there is a non-zero entry (3) after the leading 1, violating the second rule.
  - Not in RREF.

- **Matrix B**:  
  - The first row has a leading 1, and there are only zeros below and above each leading 1 in the other rows.
  - This matrix satisfies all the RREF criteria.
  - **Matrix B is in RREF**.

- **Matrix C**:  
  - The first row has a leading 1, but the second row has a non-zero entry (2) above the leading 1 in the third row.
  - Not in RREF.

- **Matrix D**:  
  - The first row has a complex number \( -i \), which is not a valid leading 1.  
  - Not in RREF.

- **Matrix E**:  
  - The first row has a leading 1, but there are non-zero entries in the same column in lower rows.
  - Not in RREF.

- **Matrix F**:  
  - The first row has a leading 1, but there is a non-zero entry (-3) after it in the first row, violating the RREF conditions.
  - Not in RREF.

### Conclusion:
- **Matrix B** is the only matrix in Reduced Row Echelon Form (RREF).

Would you like further clarification or details? Here are five related questions you might find useful:

1. What is the difference between Row Echelon Form (REF) and Reduced Row Echelon Form (RREF)?
2. Can all matrices be transformed into RREF?
3. What are the practical applications of RREF in solving linear systems?
4. How does Gaussian elimination differ from Gauss-Jordan elimination in obtaining RREF?
5. What are the conditions under which a matrix has a unique RREF?

**Tip**: When checking RREF, focus first on whether each row starts with a leading 1 and then verify that all other entries in its column are zero!

Which of the following matrices is in RREF?

Determine which matrix among the given options is in Reduced Row Echelon Form (RREF). This problem requires knowledge of matrix algebra, row reduction, and the properties of RREF. Suitable for college-level linear algebra students.

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