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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.]
Updated on: 25-Feb-2022
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