import numpy as np

A = np.array([[12, 3, 13, 6],
              [1, 15, 7, 5],
              [4, 11, 4, 8],
              [18, 2, 6, 8]])

x = np.array([[1], [2], [3], [4]])

def transformation(a, x):
    result = np.zeros((a.shape[0], x.shape[1]))
    for i in range(x.shape[0]):
        for j in range(a.shape[0]):
            result[i] += a[i, j] * x[j]
    return result

print(transformation(A, x))

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