(Solved): Solve the following system using augmented matrix methods: 2x14x23x3=2014x1 ...

Solve the following system using augmented matrix methods: $\begin{array}{c}-2x_1-4x_2-3x_3=20\\ -14x_1-28x_2-22x_3=144\\ 4x_1+8x_2+6x_3=-40\end{array}$ (a) The initial matrix is: (b) First, perform the Row Operation $\frac{1}{-2}{R}_1\to R_1$. The resulting matrix is: (c) Next, perform the operations $\begin{array}{c}+14R_1+R_2\to R_2\\ -4R_1+R_3\to R_3.\end{array}$ The resulting matrix is: (d) Finish simplifying the augmented matrix down to reduced row echelon form. The reduced matrix is: Remember: This matrix must be simplified all the way to reduced form. (e) How many solutions does the system have? If infinitely many, enter "Infinity". If none, enter 0 .