Consider the System of Equations $$\begin{array}{r}x+4 y-2 z=0 \\-2 x-6 y+5 z=5 \\3 x+14 y-4 z=8\end{array}$$

Essay

Consider the system of equations
$$\begin{array}{r}x+4 y-2 z=0 \\-2 x-6 y+5 z=5 \\3 x+14 y-4 z=8\end{array}$$
(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 $A X=B$ .