Question

Write a function matrix power(A, n) that computes the power Aⁿ using Boolean arithmetic and returns the result. You may assume that A is a 2D list containing only 0s and 1s, A is square (same number of rows and columns), and n is an integer ≥ 1. You should call your previously written matrix multiply boolean function.

Example: Let R = [ [0, 0, 0, 1], [0, 1, 1, 0], [0, 0, 0, 1], [0, 0, 1, 0] ]

Then calling matrix power(R, 2) should return [ [0, 0, 1, 0], [0, 1, 1, 1], [0, 0, 1, 0], [0, 0, 0, 1] ]

Answer 1

We initialized a boolean matrix and call the function matric_power(A,n) for calculating A^n.

Program:

Output of the program:

Source Code :

import numpy as np

# Function that using boolean arithmetic to calculate A^n
def matrix_power(A, n):
R = A
for i in range(n-1): #Loop calculates R = A^n
R = R*A
return R #It Returns the result

#Initializing 2D list A
A = np.matrix([[0,0,0,1], [0,1,1,0], [0,0,0,1], [0,0,1,0]], dtype=bool)

R = matrix_power(A,2) #Calling the function
print("Result is")
print(R.astype(int)) #Printing the result