Consider the System of Equations $$\begin{aligned}x-3 y+2 z & =5 \\2 x-4 y+3 z & =12 \\3 x-7 y+6 z & =23\end{aligned}$$

Consider the system of equations
$$\begin{aligned}x-3 y+2 z & =5 \\2 x-4 y+3 z & =12 \\3 x-7 y+6 z & =23\end{aligned}$$
(a) Write the matrix of coefficients $A$ , the matrix of variables $X$ , and the matrix of constants $B$ for this system.
(b) Find $A^{-1}$ .
(c) Use the matrix inverse method to solve the system.
(d) If the matrix of constants $B$ is replaced by the matrix $\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$ , find the solution to $A X=B$ .