Final answer:
A homogeneous system with three equations and four variables is usually underdetermined and can be assumed to have infinitely many solutions, which makes statement A) True.
Step-by-step explanation:
Whether a homogeneous system with three equations and four variables must have infinitely many solutions can be addressed by considering the number of equations relative to the number of unknowns.
In linear algebra, such a system is represented by equations of the form ax + by + cz + dw = 0, where x, y, z, and w are the variables.
In general, for a system to have a unique solution, there must be at least as many independent equations as there are variables.
If the system has fewer equations than variables, it is underdetermined and may have infinitely many solutions. However, it's important to recognize that this isn’t a guarantee—depending on the equations, a system might also have no solution.
For the case of three equations with four variables, without further information, it can typically be assumed that the system will have infinitely many solutions, as it is underdetermined. Hence, A) True is the correct answer.