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import numpy as np

def gram_schmidt_qr(A):
    n = A.shape[0]
    Q = np.zeros_like(A, dtype=np.float64)
    R = np.zeros((n, n))

    for i in range(n):
        v = A[:, i]
        for j in range(i):
            R[j, i] = np.dot(Q[:, j], A[:, i])
            v = v - R[j, i] * Q[:, j]
        R[i, i] = np.linalg.norm(v)
        Q[:, i] = v / R[i, i]
    
    return Q, R

# Example Usage
A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 10]], dtype=np.float64)
Q, R = gram_schmidt_qr(A)

print("Matrix Q (Orthogonal):")
print(Q)
print("\nMatrix R (Upper Triangular):")
print(R)