(Solved): 3. Let \( A x=b \) be a linear system whose augmented matrix has reduced row echelon form \[ \left ...

3. Let \( A x=b \) be a linear system whose augmented matrix has reduced row echelon form \[ \left(\begin{array}{rrrrr|r} 1 & 2 & 0 & -3 & 1 & 2 \\ 0 & 0 & 1 & -2 & 4 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{array}\right) \] (a). Find all solutions to the system. (b). If the first and the third column vectors of \( A \) is known as \[ a_{1}=\left(\begin{array}{l} 1 \\ 1 \\ 3 \\ 2 \end{array}\right), \quad a_{2}=\left(\begin{array}{r} 2 \\ -1 \\ -2 \\ 1 \end{array}\right), \] can we determine the vector \( b \) ? If yes, give the vector; if no, explain why.