Decide whether the linear system of equations $$A \vec{x} = \vec{b}$$ has a solution. Then find a least squares solution. $A = \begin{bmatrix} 1 & 2 \\ 0 & 4 \\ -2 & -1 \end{bmatrix}, \qquad \vec{b} = \begin{bmatrix} 1 \\ -1 \\ -3 \end{bmatrix}$