題組內容

4. Let \( A\mathbf{x} = \mathbf{b} \) be a linear system whose augmented matrix \( (A|\mathbf{b}) \) has reduced row echelon form \( \left[ \begin{array}{ccccc|c} 1 & 2 & 0 & 3 & 1 & -2 \\ 0 & 0 & 1 & 2 & 4 & 5 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{array} \right] \)

(b)(10%) If $$ a_1 = \begin{bmatrix} 1 \\ 1 \\ 3 \\ 4 \end{bmatrix} $ and  a_3 = \begin{bmatrix} 2 \\ -1 \\ 1 \\ 3 \end{bmatrix} $ determine b