If you do not mind using numpy, this is a solution
import numpy as np
matrix_A = [[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11], [12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23], [24, 25, 26, 27], [28, 29, 30, 31]]
vector_x = [0, 1, 2, 3]
res = np.sum(np.array(matrix_A) * np.array(vector_x), axis=1)
print(res)
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