how to solve python typeerror unhashable type numpyndarray

**Understanding Hashability and Mutability**

Before we get to the error itself, it's crucial to understand two fundamental concepts in Python:

1. **Hashability:**
- A "hashable" object is one that can be used as a key in a dictionary or an element in a set. Hashability is essential because dictionaries and sets use a technique called "hashing" to quickly look up and store elements. Hashing involves converting the object into an integer representation (its "hash value").
- To be hashable, an object must be *immutable*. This means its value cannot change after it's created. The hash value needs to remain consistent for the dictionary/set to function correctly.

2. **Mutability:**
- A "mutable" object is one that *can* be modified after it's created. Examples include lists, dictionaries, and NumPy arrays.
- An "immutable" object is one that *cannot* be modified after it's created. Examples include integers, floats, strings, tuples, and frozensets.

**Why NumPy Arrays are Mutable**

NumPy arrays are designed for efficient numerical computation. Mutability is often a desirable property for these arrays, as it allows you to modify the array's values in place without creating new ...

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