# Solve a linear matrix equation or system of linear scalar equations in Python

To solve a linear matrix equation, use the numpy.linalg.solve() method in Python. The method computes the “exact” solution, x, of the well-determined, i.e., full rank, linear matrix equation ax = b. Returns a solution to the system a x = b. Returned shape is identical to b. The 1st parameter a is the Coefficient matrix. The 2nd parameter b is the Ordinate or “dependent variable” values.

## Steps

At first, import the required libraries -

import numpy as np

Creating two 2D numpy arrays using the array() method. Consider the system of equations x0 + 2 * x1 = 1 and 3 * x0 + 5 * x1 = 2 −

arr1 = np.array([[1, 2], [3, 5]])
arr2 = np.array([1, 2])

Display the arrays −

print("Array1...\n",arr1)
print("\nArray2...\n",arr2)

Check the Dimensions of both the arrays −

print("\nDimensions of Array1...\n",arr1.ndim)
print("\nDimensions of Array2...\n",arr2.ndim)

Check the Shape of both the arrays −

Print(“\nShape of Array1…\n”,arr1.shape)
print("\nShape of Array2...\n",arr2.shape)

To solve a linear matrix equation, use the numpy.linalg.solve() method −

print("\nResult...\n",np.linalg.solve(arr1, arr2))

## Example

import numpy as np

# Creating two 2D numpy arrays using the array() method

# Consider the system of equations x0 + 2 * x1 = 1 and 3 * x0 + 5 * x1 = 2
arr1 = np.array([[1, 2], [3, 5]])
arr2 = np.array([1, 2])

# Display the arrays
print("Array1...\n",arr1)
print("\nArray2...\n",arr2)

# Check the Dimensions of both the arrays
print("\nDimensions of Array1...\n",arr1.ndim)
print("\nDimensions of Array2...\n",arr2.ndim)

# Check the Shape of both the arrays
print("\nShape of Array1...\n",arr1.shape)
print("\nShape of Array2...\n",arr2.shape)

# To solve a linear matrix equation, use the numpy.linalg.solve() method in Python.
print("\nResult...\n",np.linalg.solve(arr1, arr2))

## Output

Array1...
[[1 2]
[3 5]]

Array2...
[1 2]

Dimensions of Array1...
2

Dimensions of Array2...
1

Shape of Array1...
(2, 2)

Shape of Array2...
(2,)

Result...
[-1. 1.]