[Python] Increase speed of two for loops in Python

I have a double for loop in a Python code. I want to increase the execution speed, but the matrix is built using data from the previous row and column. How can I achieve this?

import numpy as np

num_rows, num_cols = 100, 5

matrix = np.zeros((num_rows, num_cols))

matrix[0, :] = np.random.rand(num_cols)
matrix[:, 0] = np.random.rand(num_rows)

coeff1 = np.random.rand(num_rows)
coeff2 = np.random.rand(num_rows)
coeff3 = np.random.rand(num_rows)

result = np.zeros_like(matrix)

for j in range(1, num_cols):
for n in range(1, num_rows):

term1 = coeff1[n] * matrix[n-1, j-1]
term2 = coeff2[n] * matrix[n, j-1]
term3 = coeff3[n] * matrix[n-1, j]

result[n, j] = term1 + term2 + term3

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