Given the matrices $A = \left( \begin{array} { c c c } 14 & 0 & 10 \\ 0 & 7 & 5 \\ 3 & 4 & 5 \alpha \end{array} \right) , \quad X = \left( \begin{array} { l } x \\ y \\ z \end{array} \right) \text{ and } \quad B = \left( \begin{array} { c } 2 \\ 37 / 2 \\ 11 \end{array} \right)$, it is requested: a) (1.25 points) Discuss the rank of matrix A, as a function of the values of the parameter $\alpha$. b) (0.75 points) For $\alpha = 0$, calculate, if possible, $A ^ { - 1 }$. c) (0.5 points) Solve, if possible, the system $A X = B$, in the case $\alpha = 0$.
Given the matrices $A = \left( \begin{array} { c c c } 14 & 0 & 10 \\ 0 & 7 & 5 \\ 3 & 4 & 5 \alpha \end{array} \right) , \quad X = \left( \begin{array} { l } x \\ y \\ z \end{array} \right) \text{ and } \quad B = \left( \begin{array} { c } 2 \\ 37 / 2 \\ 11 \end{array} \right)$, it is requested:
a) (1.25 points) Discuss the rank of matrix A, as a function of the values of the parameter $\alpha$.
b) (0.75 points) For $\alpha = 0$, calculate, if possible, $A ^ { - 1 }$.
c) (0.5 points) Solve, if possible, the system $A X = B$, in the case $\alpha = 0$.