Solve a linear matrix equation, or system of linear scalar equations.
Computes the “exact” solution, x, of the welldetermined, i.e., full rank, linear matrix equation ax = b.
Parameters:  a : array_like, shape (M, M)
b : array_like, shape (M,) or (M, N)


Returns:  x : ndarray, shape (M,) or (M, N) depending on b

Raises:  LinAlgError :

Notes
solve is a wrapper for the LAPACK routines dgesv and zgesv, the former being used if a is realvalued, the latter if it is complexvalued. The solution to the system of linear equations is computed using an LU decomposition [R50] with partial pivoting and row interchanges.
a must be square and of fullrank, i.e., all rows (or, equivalently, columns) must be linearly independent; if either is not true, use lstsq for the leastsquares best “solution” of the system/equation.
References
[R50]  (1, 2) G. Strang, Linear Algebra and Its Applications, 2nd Ed., Orlando, FL, Academic Press, Inc., 1980, pg. 22. 
Examples
Solve the system of equations 3 * x0 + x1 = 9 and x0 + 2 * x1 = 8:
>>> a = np.array([[3,1], [1,2]])
>>> b = np.array([9,8])
>>> x = np.linalg.solve(a, b)
>>> x
array([ 2., 3.])
Check that the solution is correct:
>>> (np.dot(a, x) == b).all()
True