numpy.linalg.solve¶

numpy.linalg.solve(a,b)[source]¶

Solve a linear matrix equation, or system of linear scalar equations.

Computes the “exact” solution,x, of the well-determined, i.e., fullrank, linear matrix equationax = b.

Parameters:	a : (..., M, M) array_like Coefficient matrix. b : {(..., M,), (..., M, K)}, array_like Ordinate or “dependent variable” values.
Returns:	x : {(..., M,), (..., M, K)} ndarray Solution to the system a x = b. Returned shape is identical tob.
Raises:	LinAlgError Ifa is singular or not square.

Notes

New in version 1.8.0.

Broadcasting rules apply, see thenumpy.linalg documentation fordetails.

The solutions are computed using LAPACK routine _gesv

a must be square and of full-rank, i.e., all rows (or, equivalently,columns) must be linearly independent; if either is not true, uselstsq for the least-squares best “solution” of thesystem/equation.

References

[R48]

G. Strang,Linear Algebra and Its Applications, 2nd Ed., Orlando,FL, Academic Press, Inc., 1980, pg. 22.

Examples

Solve the system of equations3*x0+x1=9 andx0+2*x1=8:

>>>a=np.array([[3,1],[1,2]])>>>b=np.array([9,8])>>>x=np.linalg.solve(a,b)>>>xarray([ 2.,  3.])

Check that the solution is correct:

>>>np.allclose(np.dot(a,x),b)True