Python Coding challenge - Day 684| What is the output of the following Python Code?

 

Code Explanation:

1. Import SymPy

from sympy import Matrix

We bring in Matrix from SymPy.

This lets us work with exact matrices for solving linear equations.

2. Define the Coefficient Matrix

A = Matrix([[2, -1,  1],

            [1,  2, -1],

            [3,  1,  1]])

This creates a 3×3 matrix representing the coefficients of 

x,y,z.

Each row corresponds to one equation.

So it encodes the system:

2x−y+z=2,x+2y−z=3,3x+y+z=7

3. Define the Constant Vector

b = Matrix([2, 3, 7])

This creates a column vector with the right-hand side constants.

It corresponds to the values after the equals sign in the equations.

4. Solve Using LU Decomposition

print(A.LUsolve(b))

SymPy internally applies LU decomposition (splits A into Lower and Upper triangular matrices).

It then performs forward and backward substitution to solve for 

x,y,z.

5. Output in Jupyter

Matrix([[1], [2], [2]])

This is how Jupyter displays the solution.

It means:

x=1,y=2,z=2

The reason it looks like a matrix is because SymPy always returns the solution as a column matrix, not a flat list.

Final Understanding

Matrix([[1], [2], [2]]) = a 3×1 column matrix.

Each row represents one solution value:

First row → 

x=1

Second row → 

y=2

Third row → 

z=2

So, the actual solution is:

(x,y,z)=(1,2,2)

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