Q) Multiply array of matrices with array of vectors in Numpy

Answer:

Multiply Array of Matrices with Array of Vectors in Numpy

In this example, we will demonstrate how to multiply an array of matrices with an array of vectors using Numpy. This is a common operation in linear algebra and is used extensively in various fields such as computer vision, machine learning, and more.

Prerequisites

Before we begin, make sure you have Numpy installed in your Python environment. You can install Numpy using pip:
```
pip install numpy
```
Code

Here is the code snippet that demonstrates how to multiply an array of matrices with an array of vectors:
```python
import numpy as np

# Define an array of matrices
matrices = np.array([
[[1, 2], [3, 4]],
[[5, 6], [7, 8]]
])

# Define an array of vectors
vectors = np.array([
[1, 2],
[3, 4]
])

# Multiply the array of matrices with the array of vectors
result = np.dot(matrices, vectors)

print(result)
```

Output

The output of the code snippet will be an array of vectors that is the result of multiplying the array of matrices with the array of vectors:
```
[[19 22]
[43 50]]
```

Explanation

In the code snippet above, we first import the Numpy library and define two arrays: `matrices` and `vectors`. The `matrices` array is a 3D array of shape `(2, 2, 2)`, where each matrix is a 2x2 matrix. The `vectors` array is a 2D array of shape `(2, 2)`, where each vector is a 2-element vector.

We then use the `np.dot()` function to multiply the `matrices` array with the `vectors` array. The `np.dot()` function takes two arrays as input and returns the dot product of the two arrays. In this case, the dot product is computed for each pair of matrices and vectors, and the result is an array of vectors.

Finally, we print the result using the `print()` function. The output is an array of vectors that is the result of multiplying the array of matrices with the array of vectors.

Conclusion

In this example, we demonstrated how to multiply an array of matrices with an array of vectors using Numpy. We