Solving linear systems (A\b) in MATLAB

Introduction

We use A\b to find the values that solve equations like Ax = b. It helps us quickly find unknowns in math problems.

When you have a set of equations and want to find the unknown values.

When you want to solve problems like finding forces, currents, or prices that fit given conditions.

When you want a fast and easy way to solve many equations at once.

When you want to check if a solution exists or find the best approximate answer.

Syntax

MATLAB

x = A \ b

A is a matrix representing coefficients of the equations.

b is a column vector representing the results of the equations.

Examples

Solves two equations with two unknowns.

MATLAB

A = [2 1; 3 4];
b = [5; 6];
x = A \ b;

Solves three equations with three unknowns.

MATLAB

A = [1 2 3; 4 5 6; 7 8 10];
b = [6; 15; 25];
x = A \ b;

Solves equations where A is singular or has infinite solutions; MATLAB gives a least squares solution.

MATLAB

A = [1 2; 2 4];
b = [3; 6];
x = A \ b;

Sample Program

This program solves the system of equations:
3x + 2y = 7
x + 4y = 10
and shows the values of x and y.

MATLAB

A = [3 2; 1 4];
b = [7; 10];
x = A \ b;
disp('Solution x:');
disp(x);

Important Notes

Use A\b instead of inv(A)*b for better speed and accuracy.

If A is not square or singular, MATLAB finds the best approximate solution.

Always check the size of A and b to match the system you want to solve.

Summary

A\b solves equations Ax = b quickly and easily.

It works for square and some non-square systems.

It is more reliable than calculating the inverse of A.