The problem in the image appears to be related to solving systems of linear equations. The first part asks you to find values of $a$, $b$, and $c$ such that the system has a:

1. Unique solution
2. No solution
3. Infinitely many solutions

Here is the given system of equations:

1. $x + y = 0$
2. $y + z = 0$
3. $x + z = 0$

Next, the second part provides a general system of linear equations with unknowns $x_1$, $x_2$, and $x_3$, and asks for the assumption that the system has a unique solution.

Would you like me to walk you through solving the first part of the problem, or would you prefer a specific focus on one of the scenarios (unique solution, no solution, infinitely many solutions)?