Introduction to Linear Algebra using MATLAB

Linear Algebra is a fundamental branch of mathematics that deals with vectors, matrices, and linear transformations, forming the backbone of

%% Introduction to Linear Algebra using MATLAB
 % Example: Solve the system of linear equations
 % 2x + 3y = 8
 % x - y = 1
 clc;        % Clear the Command Window
 clear;      % Clear all variables
 close all;  % Close all figures
 % Step 1: Define coefficient matrix A
 A = [2 3; 
     1 -1];
 % Step 2: Define constant matrix b
 b = [8; 
     1];
 % Step 3: Solve for x using matrix division (A\b)
 x = A\b;
 % Step 4: Display the result
 disp('Solution of the system A*x = b is:');
 Solution of the system A*x = b is:
 fprintf('x = %.2f\n', x(1));
 x = 2.20
 fprintf('y = %.2f\n\n', x(2));
 y = 1.20
 % Step 5: Verify the solution
 check = A*x;
 disp('Verification (A*x):');
 Verification (A*x):
 disp(check);
    8.0000
    1.0000
 disp('It should be equal to vector b:');
 It should be equal to vector b:
 disp(b);
 1
     8
     1
 % Step 6: Optional - visualize the two equations
 x_vals = -5:0.1:5; % Range for plotting
 % Equation 1: 2x + 3y = 8  => y = (8 - 2x)/3
 y1 = (8 - 2*x_vals)/3;
 % Equation 2: x - y = 1  => y = x - 1
 y2 = x_vals - 1;
 figure;
 plot(x_vals, y1, 'r', 'LineWidth', 2); hold on;
 plot(x_vals, y2, 'b', 'LineWidth', 2);
 grid on;
 xlabel('x'); ylabel('y');
 title('Graphical Solution of Linear Equations');
 legend('2x + 3y = 8', 'x - y = 1', 'Location', 'best');
 text(x(1), x(2), sprintf('  Solution (%.2f, %.2f)', x(1), x(2)), 'FontSize', 
10, 'Color', 'k');