<jupyter_start><jupyter_text>**To find the inverse of a matrix, the matrix is passed to the linalg.inv() of the NumPy module:**<jupyter_code>import numpy as np

A = np.array([[4,3],[-5,9]]) #Creation of matrix A
print(A)
inv_A = np.linalg.inv(A)
print(inv_A)
B = np.array([[20],[26]])
print(B)
X = np.linalg.inv(A).dot(B) #Multiplying the inverse of A to the dot product of B
print(X)
X = np.dot(inv_A, B) #Dot product of the given variables
print(X)<jupyter_output>[[2.]
 [4.]]<jupyter_text>**Exercise: Solving of a system of three linear equations**<jupyter_code>A = np.array([[4,3,2],[-2,2,3],[3,-5,2]])
B = np.array([[25],[-10],[-4]])
X = np.linalg.inv(A).dot(B)
print(X)<jupyter_output>[[ 5.]
 [ 3.]
 [-2.]]<jupyter_text>**Application: Word Problem**<jupyter_code>A = np.array([[20,10],[17,22]])
print(A)
inv_A = np.linalg.inv(A)
print(inv_A)
B = np.array([[350],[500]])
print(B)
X = np.dot(inv_A,B)
print(X)<jupyter_output>[[10.]
 [15.]]
{'fraction_non_alphanumeric': 0.2258748674443266, 'fraction_numerical': 0.04772004241781548, 'mean_word_length': 5.742857142857143, 'pattern_counts': {'":': 0, '<': 10, '<?xml version=': 0, '>': 10, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'chain_length': '3', 'dir': 'jupyter-structured-clean-dedup', 'id': '394519', 'license': 'Apache-2.0', 'n_tokens_mistral': 448, 'n_tokens_neox': 430, 'n_words': 90, 'path': 'Linear_Transformation.ipynb', 'repo_name': 'veronicabaron224/Linear-Algebra-58019', 'size': '943'}