(Solved): The following system has an infinite number of solutions. Form an augmented matrix, then write the ...

The following system has an infinite number of solutions. Form an augmented matrix, then write the matrix in the reduced form. Write the reduced form of the matrix below and then write the solution in terms of \( z \). \[ \begin{array}{r} 4 x+2 y+3 z=4 \\ 8 x-4 y+1 z=1 \\ 12 x-2 y+4 z=5 \end{array} \] The required augmented matrix is: \[ \left(\begin{array}{lll|l} a_{11} & a_{12} & a_{13} & b_{1} \\ a_{21} & a_{22} & a_{23} & b_{2} \\ a_{31} & a_{32} & a_{33} & b_{3} \end{array}\right) \] Where