Vector and matrix mathematics

In the previous chapter, you practiced introductory operations with vectors and matrices. In this section, you will practice more advanced vector and matrix operations that are heavily used in linear algebra. Let's remember the dot product perspective on matrix manipulation and how it can be done with different methods when you have 2-D arrays. The following code block shows alternative ways of performing dot product calculation:

In [1]: import numpy as np 
        a = np.arange(12).reshape(3,2) 
        b = np.arange(15).reshape(2,5) 
        print(a) 
        print(b)
Out[1]: 
[[ 0 1] 
 [ 2 3] 
 [ 4 5]] 
[[ 0 1 2 3 4] 
 [ 5 6 7 8 9] 
In [2]: np.dot(a,b)
Out[2]: array([[ 5,  6,  7,  8,  9], 
               [15, 20, 25, 30, 35], 
               [25, 34, 43, 52, 61]]) 
In [3]: np.matmul(a,b)
Out[3]: array([[ 5,  6,  7,  8,  9], 
               [15, 20, 25, 30...