Question

The coding must be formatted in Python.

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 initialize a boolean matrix and call the function matrix_power(A, n) to calculate A^n

Output:

Editable Code:

import numpy as np

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

The the function call we can change the second argument to calculate different powers of A

Hope this helps
If you have any doubt feel free to comment
Thank You!!