Using NumPy
Create a 5 x 3 matrix of random numbers. Create a vector of three random number.
What happens when you run matrix * vector (the product of the matrix and vector)?
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When you multiply a matrix and a vector in NumPy, the matrix is multiplied with each column of the vector. The resulting vector will have the same number of rows as the matrix.
Here's an example:
```python
import numpy as np
# Create a 5 x 3 matrix of random numbers
matrix = np.random.rand(5, 3)
print(matrix)
# Create a vector of three random numbers
vector = np.random.rand(3)
print(vector)
# Multiply matrix and vector
result = matrix * vector
print(result)
```
The output will be something like:
```
[[0.123456 0.234567 0.345678]
[0.456789 0.567890 0.678901]
[0.789012 0.890123 0.901234]
[0.012345 0.123456 0.234567]
[0.345678 0.456789 0.567890]]
[0.123 0.234 0.345]
[[0.01516229 0.05477238 0.11919319]
[0.0562678 0.13273285 0.23444786]
[0.09715504 0.20809056 0.31123201]
[0.00151803 0.02880329 0.08083025]
[0.04244819 0.10683033 0.19605398]]
```
As you can see, each column of the matrix was multiplied by the corresponding element of the vector.
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