It seems you've uploaded a mathematical problem involving matrices. Let's break down the problem into its components:

Matrix Information:

• Matrix $A = \begin{pmatrix} 14 & 0 & 10 \\ 0 & 7 & 5 \\ 3 & 4 & 5\alpha \end{pmatrix}$
• Matrix $X = \begin{pmatrix} x \\ y \\ z \end{pmatrix}$
• Matrix $B = \begin{pmatrix} \frac{37}{2} \\ 11 \end{pmatrix}$

Questions:

• a) Discuss the rank of matrix $A$ based on the parameter $\alpha$.
• b) For $\alpha = 0$, calculate if $A^{-1}$ is possible.
• c) Solve the system $AX = B$ when $\alpha = 1$.

The provided solution details:

• For part a), the rank of $A$ is 2 when $\alpha = 1$, and when $\alpha \neq 1$, the rank is 3.
• For part b), the inverse of $A$ is possible when $\alpha = 0$.
• For part c), the system $AX = B$ is solvable, and the solution is given with specific values for $x$, $y$, and $z$.

Would you like help with any particular step in solving this? Let me know if you need detailed explanations for each part or further clarification!