42.3: Review of Python Numpy Package

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from IPython.display import YouTubeVideo
YouTubeVideo("_hbWtNgstlI",width=640,height=320, cc_load_policy=True)

from IPython.display import YouTubeVideo
YouTubeVideo("_hbWtNgstlI",width=640,height=320, cc_load_policy=True)

The Python Numpy library has a “Matrix” object which can be initialized as follows:

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import numpy as np
A = np.matrix([[1,1], [20,25]])
b = np.matrix([[30],[690]])
print("A="+str(A))
print("b="+str(b))

import numpy as np
A = np.matrix([[1,1], [20,25]])
b = np.matrix([[30],[690]])
print("A="+str(A))
print("b="+str(b))

A=[[ 1  1]
 [20 25]]
b=[[ 30]
 [690]]

Python can solve equations in the $Ax=b$ format with the numpy.linalg library. For example:

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import numpy as sp

x = sp.linalg.solve(A, b)
print("X="+str(x))

import numpy as sp

x = sp.linalg.solve(A, b)
print("X="+str(x))

X=[[12.]
 [18.]]

The numpy.linalg library is just a subset of the scipy.linalg library. Oddly you can’t load the SciPy library the same way. Instead you can call it as follows:

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import scipy.linalg as la

x = la.solve(A, b)
print("X="+str(x))

import scipy.linalg as la

x = la.solve(A, b)
print("X="+str(x))

X=[[12.]
 [18.]]

Do This

Convert the following system of linear equations to numpy matrices and solve using a python linear algebra solver $18x + 21y = 22672x - 3y = 644$

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