Numpy Solving two matrices

Question

I have two matrix, A & B and i'm trying to find the Coeficients to make them fit. I know what i should be finding but i can't get anywhere close to it (Matrix C is the excpected results). I tested linear regression but I don't get the expected result

What is the way to find the good Results

import numpy as np
from sklearn.linear_model import LinearRegression



A = np.array([40, -25, 60, 0,-30,-12.5,-12.5,-30,50,30,-50])
B = np.array([[1,1,1,0,0,-1,-1,-1,0,0],
             [1,1,1,0,0,-1,-1,0,-1,0],
             [1,0,0,1,1,-1,0,0,-1,-1],
             [1,0,0,1,1,0,0,-1,-1,-1],
             [0,1,1,1,0,0,-1,-1,-1,0],
             [0,1,1,0,1,0,-1,-1,0,-1],
             [1,1,1,0,0,0,-1,0,-1,-1],
             [1,1,1,0,0,-1,0,0,-1,-1],
             [0,0,1,1,1,-1,0,0,-1,-1],
             [1,0,1,1,0,-1,-1,-1,0,0],
             [1,0,0,1,1,0,-1,-1,-1,0]])

C = np.array([-30.50,0.00,-56.00,36.50,-31.75,-65.50,-38.25,8.25,40.50,-60.75]) #expected Result
At = np.transpose(B).dot(A)
Bt = np.transpose(B).dot(B)


reg = LinearRegression().fit(Bt, At)


print("Regression result : "  + reg.coef_)

Output :

[-10.75  19.75 -36.25  56.25 -12.   -45.75 -18.5   28.    60.25 -41.  ]

Process finished with exit code 0

After Transposing :

Result :