System of equations and how to solve it

In this recipe, we will see how to solve system of equations and its applications.

Getting ready

Get the library and the numpy.linalg.solve reference.

How to do it...

We have the following functions and parameters:

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. The returned shape is identical to b.
Raises	LinAlgError If a is singular or not square.

Note

Broadcasting rules apply; see the numpy.linalg documentation for details. The solutions are computed using the LAPACK _gesv routine it must be square and of full-rank, that is, 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.

How it works...

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...