6.1 [1 pt] Write a function called indep_or_not that takes one input called vectors (a tuple...

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6.1 [1 pt] Write a function called indep_or_not that takes one input called vectors (a tuple of numpy arrays). The function should return a tuple with two elements: (i) the boolean True if the vectors are linearly independent and the boolean False otherwise, and (ii) the maximum number of linearly independent vectors among the n total vectors. The input will contain n total vectors and each vector will contain m elements (i.e. the vectors will all have the same number of elements). Your function should work for any values of n and m. In []: import numpy as np def indep_or_not(vectors): # Convert the tuple of numpy arrays to a list of numpy arrays for easier manipulation vectors = list (vectors) lab # Initialize the maximum number of linearly independent vectors to 0 max_indep_count = 0 for i in range(len(vectors)): # Create a copy of the list of vectors to check linear independence check_vectors = list (vectors) # Remove the current vector from the list to form a potential basis potential_basis = check_vectors.pop(i) # Check if the remaining vectors are linearly independent is independent = np.linalg.matrix_rank (check_vectors) == len (check_vectors) # If the remaining vectors are linearly independent, update the maximum count if is independent: max_indep_count = max(max_indep_count, len(check_vectors) + 1) # Check if the maximum count is equal to the total number of vectors are independent = max_indep_count len (vectors) return (are independent, max_indep_count) def span_or_not(vectors): # Check if the vectors span R^m by calculating the matrix rank matrix rank = np.linalg.matrix_rank(np.array(vectors).T) 6.1 [1 pt] Write a function called indep_or_not that takes one input called vectors (a tuple of numpy arrays). The function should return a tuple with two elements: (i) the boolean True if the vectors are linearly independent and the boolean False otherwise, and (ii) the maximum number of linearly independent vectors among the n total vectors. The input will contain n total vectors and each vector will contain m elements (i.e. the vectors will all have the same number of elements). Your function should work for any values of n and m. In []: import numpy as np def indep_or_not(vectors): # Convert the tuple of numpy arrays to a list of numpy arrays for easier manipulation vectors = list (vectors) lab # Initialize the maximum number of linearly independent vectors to 0 max_indep_count = 0 for i in range(len(vectors)): # Create a copy of the list of vectors to check linear independence check_vectors = list (vectors) # Remove the current vector from the list to form a potential basis potential_basis = check_vectors.pop(i) # Check if the remaining vectors are linearly independent is independent = np.linalg.matrix_rank (check_vectors) == len (check_vectors) # If the remaining vectors are linearly independent, update the maximum count if is independent: max_indep_count = max(max_indep_count, len(check_vectors) + 1) # Check if the maximum count is equal to the total number of vectors are independent = max_indep_count len (vectors) return (are independent, max_indep_count) def span_or_not(vectors): # Check if the vectors span R^m by calculating the matrix rank matrix rank = np.linalg.matrix_rank(np.array(vectors).T)