Find the reduced row echelon form of the matrix \(A = \begin{bmatrix} 1 & 2 & -1 \ 2 & 4 & -1 \ 3 & 6 & -3 \end{bmatrix}\)
Answer
Step 4: Subtract the first row from the third row: \(\begin{bmatrix} 1 & 2 & -1 \ 0 & 0 & 0 \ 0 & 0 & 1 \end{bmatrix}\)
Step 1 ：Step 1: Subtract twice the first row from the second row and thrice the first row from the third row: \(\begin{bmatrix} 1 & 2 & -1 \ 0 & 0 & 1 \ 0 & 0 & 0 \end{bmatrix}\)
Step 2 ：Step 2: Swap the second and third rows: \(\begin{bmatrix} 1 & 2 & -1 \ 0 & 0 & 0 \ 0 & 0 & 1 \end{bmatrix}\)
Step 3 ：Step 3: Add the first row to the third row: \(\begin{bmatrix} 1 & 2 & -1 \ 0 & 0 & 0 \ 1 & 2 & 0 \end{bmatrix}\)
Step 4 ：Step 4: Subtract the first row from the third row: \(\begin{bmatrix} 1 & 2 & -1 \ 0 & 0 & 0 \ 0 & 0 & 1 \end{bmatrix}\)
