(Solved): Given \( A \) and \( \mathbf{b} \) to the right, write the augmented matrix for the linear system t ...

Given \( A \) and \( \mathbf{b} \) to the right, write the augmented matrix for the linear system that corresponds to the matrix equation \( A \mathbf{x}=\mathbf{b} \). Then solve the system and write the solution as a vector. \[ A=\left[\begin{array}{rrr} 1 & 4 & -3 \\ -3 & -3 & 0 \\ 5 & 3 & 5 \end{array}\right], \mathbf{b}=\left[\begin{array}{r} -3 \\ 27 \\ -46 \end{array}\right] \] The augmented matrix for the linear system that corresponds to the matrix equation \( A \mathbf{x}=\mathbf{b} \) is Solve the system and write the solution as a vector. \[ x= \]