# file: lecture_13/p02.py
#                                                                              
# revision history:                                                            
#
# 20230928 (JP): initial version
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# Solution to the second exam problem.
#
# To run this script, do this:
#
#  python p02.py
#
#------------------------------------------------------------------------------

# import required system modules                                               
#
import os
import sys
import math
import numpy as np

#------------------------------------------------------------------------------
#
# Let's try the exam problem
#
#------------------------------------------------------------------------------

# declare a matrix X
#
A = np.array([[1, 0], [0, 1]])
print(A)
B = np.array([[0, 1], [1, 0]])
print(B)

# find rank(A), rank(B)
#
print("rank A = ", np.linalg.matrix_rank(A))
print("rank B = ", np.linalg.matrix_rank(B))

# find the rank of A+B, A-B, AB
#
print("rank A+B = ", np.linalg.matrix_rank(A + B))
print("rank A-B = ", np.linalg.matrix_rank(A - B))
print("rank A @ B = ", np.linalg.matrix_rank(A @ B))

#
# end of file