Final answer:
The heap is the suitable memory region for a dynamic and flexible array due to its capability for dynamic memory allocation. Bounds checking can be implemented by maintaining metadata for array size that is referenced every time the array is accessed to ensure indices are within valid ranges.
Step-by-step explanation:
When designing a programming language featuring dynamic and flexible arrays where the dimensions are unknown until allocation and can change afterward, the most suitable memory region for such an array would be the heap. The heap is ideal because it is designed for dynamic memory allocation, allowing arrays to be resized as needed during runtime. Stack memory, on the other hand, is not suitable due to its fixed-size nature, which requires the size of variables to be known at compile time.
For checking the bounds of the array, one approach could be to maintain metadata about the array, such as its size, which gets updated every time the array is resized. When an element is accessed, the language runtime could compare the index against this metadata to ensure it falls within the valid range. For multi-dimensional arrays, a similar check would be required for each dimension, ensuring the indices used to access the array are within the bounds of each corresponding dimension.