1. The problem asks to determine which of the given matrices are in row echelon form (REF) and which are in reduced row echelon form (RREF). 2. Matrix (g): $$\begin{pmatrix} 1 & 0 & 0 & 1 & 2 \\ 0 & 1 & 0 & 2 & 4 \\ 0 & 0 & 1 & 3 & 6 \end{pmatrix}$$ - Check for REF: Each leading entry (pivot) is 1, each pivot is to the right of the pivot in the row above, and all rows of zeros (none here) would be at the bottom. - Check for RREF: Additionally, each pivot column must have zeros in every other position. In matrix (g), the pivots are 1s at positions (1,1), (2,2), and (3,3). Columns of pivots contain zeros elsewhere, meaning pivot columns have zeros above and below the pivots. Therefore, matrix (g) satisfies both REF and RREF conditions. 3. Matrix (h): $$\begin{pmatrix} 0 & 1 & 3 & 4 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 \end{pmatrix}$$ - Check for REF: Leading entries are 1s at (1,2) and (2,3), each pivot appears to the right of the one above, and the last row is zero. - Check for RREF: In pivot columns, all other entries except the pivot must be zero. In matrix (h), the pivot columns 2 and 3 contain nonzero entries in positions other than the pivot (for example, column 2 has a 3 in row 1 which is fine, but we must check column 2 entries below pivot, there are zeros below; column 3 has 3 in row 1 which is nonzero above second pivot). Since the pivot columns contain nonzero entries other than the pivots, matrix (h) is in REF but not RREF. **Final answer:** - Matrix (g) is in reduced row echelon form. - Matrix (h) is in row echelon form but not in reduced row echelon form.