Consider the System of Equations $x+2 y-3 z=8$ $2 x+5 y-11 z=18$

Essay

Consider the system of equations
$x+2 y-3 z=8$
$2 x+5 y-11 z=18$
$3 x+7 y-13 z=24$
(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 $A X=B$ .