Final answer:
Yes, it is true that there can be a different system of fewer linear equations with the same solution set. This can be achieved by simplifying the existing system, for instance, by removing dependent equations. The answer is a) True.
Step-by-step explanation:
To answer the question: Is there a different system of fewer linear equations which has the same solution set as the system Ax? The answer is a) True. This statement is true because linear systems can often be simplified. For instance, in a system with multiple linear equations, it may be possible to eliminate one or more equations without changing the solution set. This is often done through methods such as row reduction or by combining equations to eliminate variables. Such processes can produce a simpler system that is easier to solve, yet has the same set of solutions as the original system. To illustrate, consider two equations that are scalar multiples of each other. These two equations do not provide unique information and, therefore, one can be removed without affecting the solution set. In general, any redundant or dependent equations can be excluded to simplify the system. Ultimately, as long as the remaining equations capture the necessary constraints to define the solutions, the system will maintain the same solution set.