1. The problem is to determine if the matrix \(\begin{bmatrix} 1 & 2 & 3 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}\) is in reduced row echelon form (RREF). 2. Recall the conditions for a matrix to be in RREF: - Each leading entry in a row is 1. - Each leading 1 is the only nonzero entry in its column. - The leading 1 in each row is to the right of the leading 1 in the row above. - Any rows of all zeros are at the bottom of the matrix. 3. Check the given matrix: - The first row has a leading 1 in the first column. - The second and third rows are all zeros and are at the bottom. - The leading 1 in the first row is the only nonzero entry in its column (column 1). - The leading 1 is to the right of any leading 1 in the row above (no row above first row). 4. However, the first row has nonzero entries (2 and 3) in columns 2 and 3, which are not zero. For RREF, the leading 1 must be the only nonzero entry in its column, but other columns can have nonzero entries in the same row. 5. The key is that the leading 1's column must have zeros everywhere else, which is true here since columns 2 and 3 do not have leading 1s. 6. Therefore, the matrix satisfies all RREF conditions. Final answer: Yes, the matrix is in reduced row echelon form.