1. **State the problem:** We are given matrix $$A=\begin{bmatrix}1 & 5 & 3 \\ -1 & -4 & -1 \\ -2 & -7 & 0\end{bmatrix}$$ and need to find the first row of its row-reduced echelon form (RREF), matrix $$B$$. 2. **Perform row operations to find RREF:** - Start with $$A$$: $$\begin{bmatrix}1 & 5 & 3 \\ -1 & -4 & -1 \\ -2 & -7 & 0\end{bmatrix}$$ - Add row 1 to row 2: $$R_2 \rightarrow R_2 + R_1 = (-1+1, -4+5, -1+3) = (0, 1, 2)$$ - Add 2 times row 1 to row 3: $$R_3 \rightarrow R_3 + 2R_1 = (-2+2, -7+10, 0+6) = (0, 3, 6)$$ Matrix becomes: $$\begin{bmatrix}1 & 5 & 3 \\ 0 & 1 & 2 \\ 0 & 3 & 6\end{bmatrix}$$ - Eliminate below the pivot in column 2 by subtracting 3 times row 2 from row 3: $$R_3 \rightarrow R_3 - 3R_2 = (0, 3-3, 6 - 6) = (0, 0, 0)$$ Matrix now: $$\begin{bmatrix}1 & 5 & 3 \\ 0 & 1 & 2 \\ 0 & 0 & 0\end{bmatrix}$$ - Eliminate above the pivot in row 2 by subtracting 5 times row 2 from row 1: $$R_1 \rightarrow R_1 - 5R_2 = (1, 5-5, 3 - 10) = (1, 0, -7)$$ Final RREF matrix $$B$$: $$\begin{bmatrix}1 & 0 & -7 \\ 0 & 1 & 2 \\ 0 & 0 & 0\end{bmatrix}$$ 3. **Answer:** The first row of $$B$$ is $$[1, 0, -7]$$.