`numpy.linalg:solve`

source: build-install/usr/lib/python3.14/site-packages/numpy/linalg/_linalg.py :363

Signature

def solve ( a , b )

Summary

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

Extended Summary

Computes the "exact" solution, x, of the well-determined, i.e., full rank, linear matrix equation ax = 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 (..., M) if b is shape (M,) and (..., M, K) if b is (..., M, K), where the "..." part is broadcasted between a and b.

Raises

: LinAlgError: If a is singular or not square.

Notes

Broadcasting rules apply, see the numpy.linalg documentation for details.

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, use lstsq for the least-squares best "solution" of the system/equation.

Examples

Solve the system of equations: ``x0 + 2 * x1 = 1`` and ``3 * x0 + 5 * x1 = 2``:

import numpy as np
a = np.array([[1, 2], [3, 5]])
b = np.array([1, 2])
x = np.linalg.solve(a, b)
x

✓

Check that the solution is correct:

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

`numpy.linalg:solve`

Signature

Summary

Extended Summary

Parameters

Returns

Raises

Notes

Examples

See also

Aliases

Referenced by

This package